Details of the Researcher

PHOTO

Toshiyuki Sugawa
Section
Graduate School of Information Sciences
Job title
Professor
Degree

  • 博士（理学）（京都大学）

  • 理学修士（京都大学）

Research History 3

  • 2008/04 - Present
    Tohoku University　Graduate School of Information Sciences　Professor

  • 2002/04 - 2008/03
    Hiroshima University　Graduate School of Science　Associtate Professor

  • 1991/04 - 2002/03
    Kyoto University　Graduate School of Science Division of Mathematics　Assistant

Education 3

  • Kyoto University　Graduate School of Science　Mathematics

    1990/04 - 1991/03

  • Kyoto University　Graduate School of Science　Mathematics

    1988/04 - 1990/03

  • Kyoto University　Faculty of Science

    1984/04 - 1988/03

Professional Memberships 2

  • American Mathematical Society

  • Mathematical Society of Japan

Research Interests 1

  • Complex Analysis

Research Areas 1

  • Natural sciences / Basic analysis /

Papers 87

  1. Modulus estimates of semirings with applications to boundary extension problems

    Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen

    Analysis and Mathematical Physics　15　(1)　2025/02

    DOI： 10.1007/s13324-025-01019-z 　

    ISSN： 1664-2368

    eISSN： 1664-235X

  2. UNIVERSAL CONVEXITY AND RANGE PROBLEMS OF SHIFTED HYPERGEOMETRIC FUNCTIONS

    Toshiyuki Sugawa, Li Mei Wang, Chengfa Wu

    Proceedings of the American Mathematical Society　152　(8)　3521-3535　2024/08/01

    DOI： 10.1090/proc/16849 　

    ISSN： 0002-9939

    eISSN： 1088-6826

  3. On Geometric Properties of the Ratio of Two Hypergeometric Functions

    Toshiyuki Sugawa, Li Mei Wang

    Computational Methods and Function Theory　24　(2)　241-256　2024/06

    DOI： 10.1007/s40315-023-00489-1 　

    ISSN： 1617-9447

    eISSN： 2195-3724

  4. Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity

    Oona Rainio, Toshiyuki Sugawa, Matti Vuorinen

    Journal of Geometric Analysis　34　(6)　2024/06

    DOI： 10.1007/s12220-024-01599-5 　

    ISSN： 1050-6926

  5. Nonlinear Resolvents and Decreasing Loewner Chains

    Ikkei Hotta, Sebastian Schleißinger, Toshiyuki Sugawa

    Journal of Geometric Analysis　34　(4)　2024/04

    DOI： 10.1007/s12220-023-01544-y 　

    ISSN： 1050-6926

  6. Kleinian Groups and Geometric Function Theory

    Hiroshige Shiga, Toshiyuki Sugawa

    In the Tradition of Thurston III　249-274　2024/03/19

    Publisher: Springer International Publishing

    DOI： 10.1007/978-3-031-43502-7_7 　

  7. Successive coefficients for functions in the spirallike family

    Vibhuti Arora, Saminathan Ponnusamy, Swadesh Kumar Sahoo, Toshiyuki Sugawa

    Bulletin des Sciences Mathematiques　188　2023/11

    DOI： 10.1016/j.bulsci.2023.103323 　

    ISSN： 0007-4497

  8. Moduli of quadrilaterals and quasiconformal reflection

    Semen Nasyrov, Toshiyuki Sugawa, Matti Vuorinen

    Journal of Mathematical Analysis and Applications　524　(2)　2023/08/15

    DOI： 10.1016/j.jmaa.2023.127092 　

    ISSN： 0022-247X

    eISSN： 1096-0813

  9. Conformally invariant complete metrics

    Toshiyuki Sugawa, Matti Vuorinen, Tanran Zhang

    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY　174　(2)　273-300　2022/05

    DOI： 10.1017/SO30500412200024X 　

    ISSN： 0305-0041

    eISSN： 1469-8064

  10. Geometric deduction of the solutions to modular equations

    Md Shafiul Alam, Toshiyuki Sugawa

    Ramanujan Journal　59　(2)　459-477　2022

    DOI： 10.1007/s11139-022-00604-1 　

    ISSN： 1382-4090

    eISSN： 1572-9303

  11. Harmonic spirallike functions and harmonic strongly starlike functions

    Xiu Shuang Ma, Saminathan Ponnusamy, Toshiyuki Sugawa

    Monatshefte fur Mathematik　199　(2)　363-375　2022

    DOI： 10.1007/s00605-022-01708-y 　

    ISSN： 0026-9255

  12. Intrinsic Geometry and Boundary Structure of Plane Domains

    O. Rainio, T. Sugawa, M. Vuorinen

    Siberian Mathematical Journal　62　(4)　691-706　2021/07

    DOI： 10.1134/S0037446621040121 　

    ISSN： 0037-4466

    eISSN： 1573-9260

  13. On the ninth coefficient of the inverse of a convex function

    Toshiyuki Sugawa

    Mathematics　9　(7)　2021/04

    DOI： 10.3390/math9070706 　

    eISSN： 2227-7390

  14. Sharp inequalities for logarithmic coefficients and their applications

    Saminathan Ponnusamy, Toshiyuki Sugawa

    Bulletin des Sciences Mathematiques　166　2021/02

    DOI： 10.1016/j.bulsci.2020.102931 　

    ISSN： 0007-4497

  15. On the Fourth Coefficient of the Inverse of a Starlike Function of Positive Order

    SUGAWA Toshiyuki, WANG Li-Mei

    Interdisciplinary Information Sciences　27　(1)　93-106　2021

    Publisher: Graduate School of Information Sciences, Tohoku University

    DOI： 10.4036/iis.2021.R.01 　

    ISSN： 1340-9050

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    <p>We consider the inverse function z = g(w) of a (normalized) starlike function w = f(z) of order α on the unit disk of the complex plane with 0 < α < 1. Krzyż, Libera and Złotkiewicz obtained sharp estimates of the second and the third coefficients of g(w) in their paper (1979). Prokhorov and Szynal gave sharp estimates of the fourth coefficient of g(w) as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of g(w) together with explicit forms of the extremal functions.</p>

  16. Teichmüller’s Theorem in Higher Dimensions and Its Applications

    Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen

    Computational Methods and Function Theory　20　(3-4)　539-558　2020/11

    DOI： 10.1007/s40315-020-00340-x 　

    ISSN： 1617-9447

    eISSN： 2195-3724

  17. On the hyperbolic distance of n-times punctured spheres

    Toshiyuki Sugawa, Matti Vuorinen, Tanran Zhang

    Journal d'Analyse Mathematique　141　(2)　663-687　2020/09

    DOI： 10.1007/s11854-020-0112-9 　

    ISSN： 0021-7670

    eISSN： 1565-8538

  18. Aharonov invariants revisited

    Toshiyuki Sugawa

    Analysis and Mathematical Physics　10　(3)　2020/09/01

    DOI： 10.1007/s13324-020-00374-3 　

    ISSN： 1664-2368

    eISSN： 1664-235X

  19. Geometric properties of the nonlinear resolvent of holomorphic generators

    Mark Elin, David Shoikhet, Toshiyuki Sugawa

    Journal of Mathematical Analysis and Applications　483　(2)　2020/03/15

    DOI： 10.1016/j.jmaa.2019.123614 　

    ISSN： 0022-247X

    eISSN： 1096-0813

  20. Schur Parameters and the Carathéodory Class

    Ming Li, Toshiyuki Sugawa

    Results in Mathematics　74　(4)　2019/12/01

    DOI： 10.1007/s00025-019-1107-7 　

    ISSN： 1422-6383

    eISSN： 1420-9012

  21. Hornich Operations on Functions of Bounded Boundary Rotations and Order α

    Saminathan Ponnusamy, Swadesh Kumar Sahoo, Toshiyuki Sugawa

    Computational Methods and Function Theory　19　(3)　455-472　2019/09/01

    DOI： 10.1007/s40315-019-00276-x 　

    ISSN： 1617-9447

    eISSN： 2195-3724

  22. Characterizations for Inner Functions in Certain Function Spaces

    Atte Reijonen, Toshiyuki Sugawa

    Complex Analysis and Operator Theory　13　(4)　1853-1871　2019/06/01

    DOI： 10.1007/s11785-018-0863-9 　

    ISSN： 1661-8254

    eISSN： 1661-8262

  23. A construction of trivial beltrami coefficients

    Toshiyuki Sugawa

    Proceedings of the American Mathematical Society　147　(2)　629-635　2019/02

    DOI： 10.1090/proc/13965 　

    ISSN： 0002-9939

    eISSN： 1088-6826

  24. An Extremal Problem for Univalent Functions

    SUGAWA Toshiyuki, WANG Li-Mei

    Interdisciplinary Information Sciences　25　(1)　45-52　2019

    Publisher: Graduate School of Information Sciences, Tohoku University

    DOI： 10.4036/iis.2019.A.04 　

    ISSN： 1340-9050

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    <p>For a real constant b, we give sharp estimates of log |f(z)/z|+b arg[f(z)/z] for subclasses of normalized univalent functions f on the unit disk.</p>

  25. Hereditarily non uniformly perfect sets

    Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi

    Discrete and Continuous Dynamical Systems - Series S　13　(2)　2391-2402　2019

    DOI： 10.3934/dcdss.2019150 　

    ISSN： 1937-1632

    eISSN： 1937-1179

  26. Construction of nearly hyperbolic distance on punctured spheres

    Toshiyuki Sugawa, Tanran Zhang

    Bulletin of Mathematical Sciences　8　(2)　307-323　2018/08/01

    DOI： 10.1007/s13373-017-0111-z 　

    ISSN： 1664-3607

    eISSN： 1664-3615

  27. Coefficient estimates of analytic endomorphisms of the unit disk fixing a point with applications to concave functions Peer-reviewed

    Rintaro Ohno, Toshiyuki Sugawa

    Kyoto Journal of Mathematics　58　(2)　227-241　2018/06/01

    DOI： 10.1215/21562261-2017-0015 　

    ISSN： 2156-2261

  28. Filtration of Semi-complete Vector Fields Revisited

    Mark Elin, David Shoikhet, Toshiyuki Sugawa

    Trends in Mathematics　(9781493976584)　93-102　2018

    DOI： 10.1007/978-3-319-70154-7_6 　

    ISSN： 2297-0215

    eISSN： 2297-024X

  29. Geometric Properties of the Shifted Hypergeometric Functions Peer-reviewed

    Toshiyuki Sugawa, Li Mei Wang

    Complex Analysis and Operator Theory　11　(8)　1879-1893　2017/12/01

    DOI： 10.1007/s11785-017-0674-4 　

    ISSN： 1661-8254

    eISSN： 1661-8262

  30. A Note on Successive Coefficients of Convex Functions

    Ming Li, Toshiyuki Sugawa

    Computational Methods and Function Theory　17　(2)　179-193　2017/06/01

    DOI： 10.1007/s40315-016-0177-8 　

    ISSN： 1617-9447

  31. Spirallikeness of shifted hypergeometric functions

    Toshiyuki Sugawa, Li Mei Wang

    Annales Academiae Scientiarum Fennicae Mathematica　42　963-977　2017

    DOI： 10.5186/AASFM.2017.4257 　

    ISSN： 1239-629X

    eISSN： 1798-2383

  32. ANALYTIC AND GEOMETRIC PROPERTIES OF OPEN DOOR FUNCTIONS Peer-reviewed

    Ming Li, Toshiyuki Sugawa

    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY　54　(1)　267-280　2017/01

    DOI： 10.4134/JKMS.j150720 　

    ISSN： 0304-9914

    eISSN： 2234-3008

  33. Spherical convexity and hyperbolic metric

    Toshiyuki Sugawa

    Journal of Analysis　24　(1)　167-175　2016/06/01

    Publisher: Springer Science and Business Media B.V.

    DOI： 10.1007/s41478-016-0013-6 　

    ISSN： 0971-3611

  34. QUASICONFORMAL EXTENSION OF MEROMORPHIC FUNCTIONS WITH NONZERO POLE Peer-reviewed

    B. Bhowmik, G. Satpati, T. Sugawa

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY　144　(6)　2593-2601　2016/06

    DOI： 10.1090/proc/12933 　

    ISSN： 0002-9939

    eISSN： 1088-6826

  35. Notes on Convex Functions of Order alpha Peer-reviewed

    Toshiyuki Sugawa, Li-Mei Wang

    COMPUTATIONAL METHODS AND FUNCTION THEORY　16　(1)　79-92　2016/03

    DOI： 10.1007/s40315-015-0122-2 　

    ISSN： 1617-9447

    eISSN： 2195-3724

  36. Variability regions of close-to-convex functions Peer-reviewed

    Takao Kato, Toshiyuki Sugawa, Li-Mei Wang

    ANNALES POLONICI MATHEMATICI　111　(1)　89-105　2014

    DOI： 10.4064/ap111-1-7 　

    ISSN： 0066-2216

    eISSN： 1730-6272

  37. Univalence criteria and analogues of the John constant Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    Bulletin of the Australian Mathematical Society　88　(3)　423-434　2013/12

    DOI： 10.1017/S0004972712000962 　

    ISSN： 0004-9727 1755-1633

  38. On mu-conformal homeomorphisms and boundary correspondence Peer-reviewed

    Vladimir Gutlyanskii, Ken-ichi Sakan, Toshiyuki Sugawa

    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS　58　(7)　947-962　2013/07

    DOI： 10.1080/17476933.2011.613116 　

    ISSN： 1747-6933

  39. Univalent Functions with Half-Integral Coefficients Peer-reviewed

    Naoki Hiranuma, Toshiyuki Sugawa

    COMPUTATIONAL METHODS AND FUNCTION THEORY　13　(1)　133-151　2013

    DOI： 10.1007/s40315-013-0009-z 　

    ISSN： 1617-9447

  40. On univalence of the power deformation z(f(z)/z)(c) Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    CHINESE ANNALS OF MATHEMATICS SERIES B　33　(6)　823-830　2012/11

    DOI： 10.1007/s11401-012-0750-z 　

    ISSN： 0252-9599

  41. On power deformations of univalent functions Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    MONATSHEFTE FUR MATHEMATIK　167　(2)　231-240　2012/08

    DOI： 10.1007/s00605-011-0344-y 　

    ISSN： 0026-9255

  42. Correspondence between spirallike functions and starlike functions Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    MATHEMATISCHE NACHRICHTEN　285　(2-3)　322-331　2012/02

    DOI： 10.1002/mana.201010020 　

    ISSN： 0025-584X

  43. A Remark on Löwner's Theorem

    SUGAWA Toshiyuki

    Interdisciplinary Information Sciences　18　(1)　19-22　2012

    Publisher: The Editorial Committee of the Interdisciplinary Information Sciences

    DOI： 10.4036/iis.2012.19 　

    ISSN： 1340-9050

    More details Close

    We give a refinement of Löwner's inequality with argument of the equality case. To this end, we establish a complete univalence criterion for meromorphic functions of special type. We also give applications of the refinement.

  44. On a Multi-Point Schwarz-Pick Lemma Peer-reviewed

    Kyung Hyun Cho, Seong-A Kim, Toshiyuki Sugawa

    COMPUTATIONAL METHODS AND FUNCTION THEORY　12　(2)　483-499　2012

    DOI： 10.1007/BF03321839 　

    ISSN： 1617-9447

  45. Quasiconformal Extension of Strongly Spirallike Functions Peer-reviewed

    Toshiyuki Sugawa

    COMPUTATIONAL METHODS AND FUNCTION THEORY　12　(1)　19-30　2012

    ISSN： 1617-9447

  46. Invariant Schwarzian Derivatives of Higher Order Peer-reviewed

    Seong-A Kim, Toshiyuki Sugawa

    COMPLEX ANALYSIS AND OPERATOR THEORY　5　(3)　659-670　2011/09

    DOI： 10.1007/s11785-010-0081-6 　

    ISSN： 1661-8254

  47. Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky Peer-reviewed

    Daniela Kraus, Oliver Roth, Toshiyuki Sugawa

    MATHEMATISCHE ZEITSCHRIFT　267　(3-4)　851-868　2011/04

    DOI： 10.1007/s00209-009-0649-x 　

    ISSN： 0025-5874

  48. GEOMETRIC INVARIANTS ASSOCIATED WITH PROJECTIVE STRUCTURES AND UNIVALENCE CRITERIA Peer-reviewed

    Seong-A Kim, Toshiyuki Sugawa

    TOHOKU MATHEMATICAL JOURNAL　63　(1)　41-57　2011/03

    DOI： 10.2748/tmj/1303219935 　

    ISSN： 0040-8735

  49. Sharp norm estimate of Schwarzian derivative for a class of convex functions Peer-reviewed

    Stanislawa Kanas, Toshiyuki Sugawa

    ANNALES POLONICI MATHEMATICI　101　(1)　75-86　2011

    DOI： 10.4064/ap101-1-8 　

    ISSN： 0066-2216

    eISSN： 1730-6272

  50. HARDY SPACES AND UNBOUNDED QUASIDISKS Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA　36　(1)　291-300　2011

    DOI： 10.5186/aasfm.2011.3618 　

    ISSN： 1239-629X

  51. A conformally invariant metric on Riemann surfaces associated with integrable holomorphic quadratic differentials Peer-reviewed

    Toshiyuki Sugawa

    MATHEMATISCHE ZEITSCHRIFT　266　(3)　645-664　2010/11

    DOI： 10.1007/s00209-009-0590-z 　

    ISSN： 0025-5874

  52. Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral Peer-reviewed

    G. D. Anderson, T. Sugawa, M. K. Vamanamurthy, M. Vuorinen

    MATHEMATISCHE ZEITSCHRIFT　266　(1)　181-191　2010/09

    DOI： 10.1007/s00209-009-0560-5 　

    ISSN： 0025-5874

  53. Dual mean value problem for complex polynomials Peer-reviewed

    Vladimir Dubinin, Toshiyuki Sugawa

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES　85　(9)　135-137　2009/11

    DOI： 10.3792/pjaa.85.135 　

    ISSN： 0386-2194

  54. A NOTE ON BAZILEVIC FUNCTIONS Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    TAIWANESE JOURNAL OF MATHEMATICS　13　(5)　1489-1495　2009/10

    ISSN： 1027-5487

  55. Completely monotone sequences and universally prestarlike functions Peer-reviewed

    Stephan Ruscheweyh, Luis Salinas, Toshiyuki Sugawa

    ISRAEL JOURNAL OF MATHEMATICS　171　(1)　285-304　2009/06

    DOI： 10.1007/s11856-009-0050-9 　

    ISSN： 0021-2172

  56. Uniformly locally univalent functions and Hardy spaces Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　353　(1)　61-67　2009/05

    DOI： 10.1016/j.jmaa.2008.11.036 　

    ISSN： 0022-247X

  57. A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions Peer-reviewed

    Toshiyuki Sugawa, Takao Terada

    MONATSHEFTE FUR MATHEMATIK　156　(2)　167-173　2009/02

    DOI： 10.1007/s00605-008-0548-y 　

    ISSN： 0026-9255

  58. NORM ESTIMATES AND UNIVALENCE CRITERIA FOR MEROMORPHIC FUNCTIONS Peer-reviewed

    Saminathan Ponnusamy, Toshiyuki Sugawa

    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY　45　(6)　1661-1676　2008/11

    ISSN： 0304-9914

    eISSN： 2234-3008

  59. A note on a theorem of Chuaqui and Gevirtz Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA　33　(1)　273-279　2008

    ISSN： 1239-629X

  60. The limiting shape of one-dimensional Teichmuller spaces Peer-reviewed

    Toshiyuki Sugawa

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY　136　(8)　2849-2858　2008

    DOI： 10.1090/S0002-9939-08-09428-8 　

    ISSN： 0002-9939

  61. Strong starlikeness for a class of convex functions Peer-reviewed

    Stanislawa Kanas, Toshiyuki Sugawa

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　336　(2)　1005-1017　2007/12

    DOI： 10.1016/j.jmaa.2007.03.025 　

    ISSN： 0022-247X

  62. A general approach to the Fekete-Szego problem Peer-reviewed

    Jae Ho Choi, Yong Chan Kim, Toshiyuki Sugawa

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　59　(3)　707-727　2007/07

    DOI： 10.2969/jmsj/05930707 　

    ISSN： 0025-5645

  63. Invariant differential operators associated with a conformal metric Peer-reviewed

    Seong-A Kim, Toshiyuki Sugawa

    MICHIGAN MATHEMATICAL JOURNAL　55　(2)　459-479　2007

    DOI： 10.1307/mmj/1187647003 　

    ISSN： 0026-2285

  64. The Alexander transform of a spirallike function Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　325　(1)　608-611　2007/01

    DOI： 10.1016/j.jmaa.2006.01.077 　

    ISSN： 0022-247X

  65. Geometric function theory and Smale's mean value conjecture Peer-reviewed

    Ege Fujikawa, Toshiyuki Sugawa

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES　82　(7)　97-100　2006/09

    ISSN： 0386-2194

  66. Norm estimates of the pre-Schwarzian derivatives for certain classes of univalent functions Peer-reviewed

    YC Kim, T Sugawa

    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY　49　(Part 1)　131-143　2006/02

    DOI： 10.1017/S0013091504000306 　

    ISSN： 0013-0915

  67. A Conformal invariant for nonvanishing analytic functions and its applications Peer-reviewed

    Yong Chan Kim, Toshiyuki Sugawa

    MICHIGAN MATHEMATICAL JOURNAL　54　(2)　393-410　2006

    DOI： 10.1307/mmj/1156345602 　

    ISSN： 0026-2285

  68. On conformal representations of the interior of an ellipse Peer-reviewed

    Stanislawa Kanas, Toshiyuki Sugawa

    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA　31　(2)　329-348　2006

    ISSN： 1239-629X

  69. Drawing Bers embeddings of the Teichmuller space of once-punctured tori Peer-reviewed

    Y Komori, T Sugawa, M Wada, Y Yamashita

    EXPERIMENTAL MATHEMATICS　15　(1)　51-60　2006

    DOI： 10.1080/10586458.2006.10128951 　

    ISSN： 1058-6458

  70. Characterizations of hyperbolically convex regions Peer-reviewed

    SA Kim, T Sugawa

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　309　(1)　37-51　2005/09

    DOI： 10.1016/j.jmaa.2004.12.008 　

    ISSN： 0022-247X

  71. Some inequalities for the Poincare metric of plane domains Peer-reviewed

    T Sugawa, M Vuorinen

    MATHEMATISCHE ZEITSCHRIFT　250　(4)　885-906　2005/08

    DOI： 10.1007/s00209-005-0782-0 　

    ISSN： 0025-5874

  72. Norm estimates for the Alexander transforms of convex functions of order alpha Peer-reviewed

    JH Choi, YC Kim, S Ponnusamy, T Sugawa

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　303　(2)　661-668　2005/03

    DOI： 10.1016/j.jmaa.2004.08.066 　

    ISSN： 0022-247X

  73. On the degenerate Beltrami equation Peer-reviewed

    Gutlyanskii, V, O Martio, T Sugawa, M Vuorinen

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY　357　(3)　875-900　2005

    DOI： 10.1090/S0002-9947-04-03708-0 　

    ISSN： 0002-9947

  74. Mapping properties of nonlinear integral operators and pre-Schwarzian derivatives Peer-reviewed

    YC Kim, S Ponnusamy, T Sugawa

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　299　(2)　433-447　2004/11

    DOI： 10.1016/j.jmaa.2004.03.081 　

    ISSN： 0022-247X

  75. Geometric properties of nonlinear integral transforms of certain analytic functions Peer-reviewed

    YC Kim, S Ponnusamy, T Sugawa

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES　80　(5)　57-60　2004/05

    ISSN： 0386-2194

  76. Some counterexamples in dynamics of rational semigroups Peer-reviewed

    R Stankewitz, T Sugawa, H Sumi

    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA　29　(2)　357-366　2004

    ISSN： 1239-629X

  77. Existence and uniqueness theorems for the Beltrami equation with degeneration Peer-reviewed

    M Viorinen, VY Gutlyanskii, O Martio, T Sugawa

    DOKLADY MATHEMATICS　68　(3)　313-315　2003/11

    ISSN： 1064-5624

  78. Growth and coefficient estimates for uniformly locally univalent functions on the unit disk Peer-reviewed

    Yong Chang Kim, Toshiyuki Sugawa

    Rocky Mountain Journal of Mathematics　32　(1)　179-200　2002

    DOI： 10.1216/rmjm/1030539616 　

    ISSN： 0035-7596

  79. 一様完全集合 - その解析的 ・ 幾何的側面 -

    須川 敏幸

    数学　53　(4)　387-402　2001/10/01

    Publisher: The Mathematical Society of Japan

    DOI： 10.11429/sugaku1947.53.387 　

    ISSN： 0039-470X

  80. An explicit bound for uniform perfectness of the Julia sets of rational maps Peer-reviewed

    T Sugawa

    MATHEMATISCHE ZEITSCHRIFT　238　(2)　317-333　2001/10

    DOI： 10.1007/s002090100255 　

    ISSN： 0025-5874

  81. Uniform perfectness of the limit sets of Kleinian groups Peer-reviewed

    T Sugawa

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY　353　(9)　3603-3615　2001

    DOI： 10.1090/S0002-9947-01-02775-1 　

    ISSN： 0002-9947

  82. Coefficient bounds and convolution properties for certain classes of close-to-convex functions Peer-reviewed

    YC Kim, JH Choi, T Sugawa

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES　76　(6)　95-98　2000/06

    ISSN： 0386-2194

  83. Uniform Perfectness of the Julia Sets of Quadratic Polynomials

    Science bulletin of Josai University, Special Issue　4　47-56　1998

    Publisher:

    DOI： 10.20566/13429590_4_47 　

    ISSN： 1342-9590

  84. Various domain constants related to uniform perfectness

    Sugawa Toshiyuki

    Complex Variables Theory and Application　36　(4)　311-345　1998

    Publisher: Taylor & Francis

    ISSN： 0278-1077

  85. On the space of schlicht projective structures on compact Riemann surfaces with boundary Peer-reviewed

    T Sugawa

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY　35　(4)　697-732　1995/12

    ISSN： 0023-608X

  86. THE BERS PROJECTION AND THE LAMBDA-LEMMA Peer-reviewed

    T SUGAWA

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY　32　(4)　701-713　1992/12

    ISSN： 0023-608X

  87. ON THE BERS CONJECTURE FOR FUCHSIAN-GROUPS OF THE 2ND KIND Peer-reviewed

    SUGAWA T

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY　32　(1)　45-52　1992

    ISSN： 0023-608X

Show all ︎Show first 5

Misc. 22

  1. 微積分から始まる解析学の厳密性 複素解析の闇を探る

    須川敏幸

    数理科学　61　(4)　2023

    ISSN： 0386-2240

  2. 複素解析におけるポテンシャル論—特集 ポテンシャルを探る

    須川 敏幸

    数理科学　60　(3)　35-41　2022/03

    Publisher: サイエンス社

    ISSN： 0386-2240

  3. 書評 志賀啓成 : リーマンと解析学,リーマンの生きる数学(黒川信重編),2,共立出版,2020年,ⅷ+98ページ

    須川 敏幸

    数学 / 日本数学会 編　74　(3)　331-334　2022

    ISSN： 0039-470X

  4. 複素双曲空間入門—特集 非ユークリッド幾何学の数理

    須川 敏幸

    数理科学　59　(4)　16-23　2021/04

    Publisher: サイエンス社

    ISSN： 0386-2240

  5. 複素数ってそもそも何なの?—特集 複素関数の質問箱

    須川 敏幸

    数学セミナー　57　(6)　8-12　2018/06

    Publisher: 日本評論社

    ISSN： 0386-4960

  6. 複素解析—特集 分野を語る10の定理

    須川 敏幸

    数学セミナー　56　(8)　28-32　2017/08

    Publisher: 日本評論社

    ISSN： 0386-4960

  7. ワイルとリーマン面—特集 ワイル : 現代の数学と物理に与えた影響を探る

    須川 敏幸

    数理科学　54　(10)　15-21　2016/10

    Publisher: サイエンス社

    ISSN： 0386-2240

  8. エレガントな解答をもとむ 解答 : 出題 2015年2月号

    須川 敏幸, 徳重 典英, 竹縄 知之

    数学セミナー　54　(5)　90-99　2015/05

    Publisher: 日本評論社

    ISSN： 0386-4960

  9. リーマン面の分岐被覆—特集 被覆のはなし

    須川 敏幸

    数学セミナー　52　(1)　24-29　2013/01

    Publisher: 日本評論社

    ISSN： 0386-4960

  10. 複素関数論への招待—特集 大学数学が一望できる数学ランドへようこそ(その1)

    須川 敏幸

    数学セミナー　50　(5)　44-49　2011/05

    Publisher: 日本評論社

    ISSN： 0386-4960

  11. エレガントな解答をもとむ 解答--出題 2010年12月号

    有澤 誠, 須川 敏幸

    数学セミナー　50　(3)　98-106　2011/03

    Publisher: 日本評論社

    ISSN： 0386-4960

  12. 書評 E. de Faria and W. de Melo: Mathematical tools for one-dimensional dynamics

    須川 敏幸

    数学 / 日本数学会 編　63　(3)　363-366　2011

    Publisher: 日本数学会

    ISSN： 0039-470X

    More details Close

    記事種別: 書評

  13. エレガントな解答をもとむ 解答--出題 2009年4月号

    須川 敏幸, 萩田 真理子

    数学セミナー　48　(7)　86-93　2009/07

    Publisher: 日本評論社

    ISSN： 0386-4960

  14. エレガントな解答をもとむ 解答--出題 2008年4月号

    須川 敏幸, 中内 伸光

    数学セミナー　47　(7)　102-108　2008/07

    Publisher: 日本評論社

    ISSN： 0386-4960

  15. 数列の極限—特集 極限--知れば知るほど深まる数学

    須川 敏幸

    数学セミナー　46　(6)　12-16　2007/06

    Publisher: 日本評論社

    ISSN： 0386-4960

  16. 書評 谷口雅彦:フラクタル曲線についての解析学--擬等角写像外伝

    須川 敏幸

    数学 / 日本数学会 編　59　(1)　105-108　2007/01

    Publisher: 日本数学会

    ISSN： 0039-470X

    More details Close

    記事種別: 書評

  17. ON UNIVALENCE CRITERIA FOR MEROMORPHIC FUNCTIONS (Coefficient Inequalities in Univalent Function Theory and Related Topics)

    Sugawa Toshiyuki

    RIMS Kokyuroku　1414　117-122　2005/02

    Publisher: Kyoto University

    ISSN： 1880-2818

  18. DRAWING BERS EMBEDDINGS OF THE TEICHMULLER SPACE OF ONCE PUNCTURED TORI (Hyperbolic Spaces and Related Topics II)

    Komori Yohei, Sugawa Toshiyuki, Wada Masaaki, Yamashita Yasushi

    RIMS Kokyuroku　1163　9-17　2000/07

    Publisher: Kyoto University

    ISSN： 1880-2818

  19. INNER RADIUS OF UNIVALENCE FOR A STRONGLY STARLIKE DOMAIN (New Extension of Historical Theorems for Univalent Function Theory)

    Sugawa Toshiyuki

    RIMS Kokyuroku　1164　144-150　2000/07

    Publisher: Kyoto University

    ISSN： 1880-2818

  20. On an application of ribbon graphs to resolution of the Branch singularities of Hyeperbolic 2-ORBIFOLDS (Hyperbolic Spaces and Related Topics)

    Sugawa Toshiyuki

    RIMS Kokyuroku　1104　25-29　1999/07

    Publisher: Kyoto University

    ISSN： 1880-2818

  21. A GEOMETRIC PROOF OF SELBERG'S LEMMA FOR FUCHSIAN GROUPS (Analysis and Geometry of Hyperbolic Spaces)

    Sugawa Toshiyuki

    RIMS Kokyuroku　1065　1-13　1998/10

    Publisher: Kyoto University

    ISSN： 1880-2818

  22. GROWTH AND COEFFICIENT ESTIMATES FOR UNIFORMLY LOCALLY UNIVALENT FUNCTIONS ON THE UNIT DISK (Applications of Complex Function Theory to Differential Equations)

    Kim Yong Chan, Sugawa Toshiyuki

    RIMS Kokyuroku　1062　34-46　1998/09

    Publisher: Kyoto University

    ISSN： 1880-2818

Show all ︎Show first 5

Books and Other Publications 2

  1. 複素解析学特論

    楠, 幸男, 須川, 敏幸

    現代数学社　2019/11

    ISBN: 9784768705209

  2. Topics in Finite or Infinite Dimensional Complex Analysis

    Katsuhiko Matsuzaki, Toshiyuki Sugawa

    Tohoku University Press　2013/01

    More details Close

    Proceedings of the 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, held in Hiroshima, 2011.

Research Projects 31

  1. Quasiconformal extension in differential geometry and theory of the universal Teichmueller space in harmonic analysis

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Waseda University

    2018/04/01 - 2023/03/31

  2. Analysis of elliptic operators and its applications to Geometric Function Theory

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2017/04/01 - 2022/03/31

  3. 複雑領域のポテンシャル解析の深化―非線形PDEと理想境界への応用

    相川 弘明, 志賀 啓成, 倉田 和浩, 須川 敏幸, 平田 賢太郎, 鈴木 紀明, 正宗 淳, 利根川 吉廣, 木上 淳, 加須栄 篤, 堀田 一敬, 野瀬 敏洋

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(A)

    2017/04/01 - 2021/03/31

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    Intrinsic ultracontractivity を応用して，Lipschitz領域やJohn領域をベースにするシリンダー上の熱方程式の優解の可積分性を与え，正値優調和関数の可積分性を放物型に拡張した．境界条件付きの一般化された平均曲率流であるBrakke流の時間大域解存在を証明した．非線形無限ネットワークのラプラシアンを研究し，リウヴィユ性，カシミンスキー条件，Omori-Yauタイプの弱最大値原理などの同値性や正値優調和関数の最小増大度，具体的判定条件について成果を得た．パターン形成に関わるFitzHugh反応拡散系のヘテロクリニック定常解の構成とエネルギー漸近展開を行なった. 3波相互作用を持つ非線形シュレディンガー方程式系に現れる変分問題のエネルギー最小解の存在とその漸近挙動に関する知見を得た.領域の境界の一様完全性や領域の一様性の新しいポテンシャル論的特徴づけを得た．有界Lipschitz領域において，半線形楕円型方程式の正値解に対する境界Harnack原理を，Greenポテンシャルの評価と反復法を用いて示した．孤立境界特異点をもつ正値解の漸近挙動および除去可能性について考察した．自己相似集合の Ahlfors regular conformal dimension と対応する無限グラフの parabolic index の関係および自己相似集合上への p-energy の構成について研究し，parabolic index とAhlfors regular conformal dimension の間の不等式などを示した．ポテンシャル付きの二階楕円型作用素の保存則を定式化して，対応するカシミンスキー・テストを証明した．均質化法のH収束理論を多様体に拡張し，作用素の収束を実現するリーマン計量ならびに複雑な空間への収束する多様体の族の変形理論を構築した．

  4. Degeneration and collapsing of Kleinian groups; geometry and analysis of the compactification of their defamation spaces

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    2016/04/01 - 2021/03/31

  5. Research on the Weil-Petersson metric of infinite dimensional Teichmueller spaces

    Matsuzaki Katsuhiko, YANAGISHITA Masahiro

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Waseda University

    2013/04/01 - 2019/03/31

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    We introduced the Teichmueller space of diffeomorphisms of the unit circle with Hoelder continuous derivatives as a subspace of the universal Teichmueller space. We provided a complex Banach manifold structure for it and proved that its topology coincides with the one induced by the Hoelder constants of the maps. We also proved that the barycentric extension induces a continuous section from the Teichmueller space of the circle diffeomorphisms with respect to this topology. Then, we considered deformations of a group of circle diffeomorphisms with Hoelder continuous derivative and showed certain rigidity under conjugation by symmetric homeomorphisms of the circle. As an application, we give a condition for such a diffeomorphism group to be conjugate to a Moebius group by a diffeomorphism of the same regularity. The strategy is to find a fixed point of the group which acts isometrically on the integrable Teichmueller space with the Weil-Petersson metric.

  6. Toward the construction of a new kind of Teichmueller space and its analysis

    SUGAWA Toshiyuki, Zhang Tanran, Wang Li-Mei

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research

    Category: Grant-in-Aid for Challenging Exploratory Research

    Institution: Tohoku University

    2015/04/01 - 2018/03/31

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    One can assign N pairs of sides to a polygon with 2N sides in the plane. Pasting each pair of sides by a complex affine map yields a Riemann surface with affine structure. Our purpose was to construct a suitable vector bundle over the Teichmueller space which describes those Riemann surfaces arising from this construction. It turns out that it is equivalent to consider the space of affine representations of the fundamental group of a fixed Riemann surface with punctures. Moreover, if the sides have the same length for each pair in the above construction, one obtains a singular Euclidean structure for the Riemann surface. Therefore, we understand that a moduli space of such objects can be understood as a section of the above vector bundle.

  7. Potential theory on space complexity and ideal boundary

    Aikawa Hiroaki, KUMAGAI TAKASHI

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Hokkaido University

    2013/04/01 - 2017/03/31

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    Relationships among harmonic functions, solutions to the heat equation, the Green and heat kernels and their defining domains, the influence of the space complexity to the boundary behavior were studied. They were applied to various fields such as non-smooth Euclidean domains, manifolds, varifolds, networks and fractals. In particular, new results were obtained in Harnack principle with exceptional sets, estimates of the principal frequency in terms of capacitary width, sufficient conditions for the global boundary Harnack principle based on the capacitary width of sublevel sets of the Green function, conditions for the parabolic boundary Harnack principle (Intrinsic Ultracontractivity), the critical exponent of a graph domain enjoying the global boundary Harnack principle, and the 0-1 law of the capacity density at infinity and so on.

  8. Analysis of degenerations and singularities of Kleinian groups and complex dynamics

    SHIGA Hiroshige, AIKAWA Hiroaki, SHISHIKURA Mitsuhiro, SUGAWA Toshiyuki, ASHIKAGA Tadashi, OHSHIKA Ken'ichi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tokyo Institute of Technology

    2010/04/01 - 2015/03/31

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    By developing the research of the complex structure of the deformation space of a Kleinian group, we find many complex analytic properties of the deformation space. We also find a relationship between the infectivity radius of a point in the moduli space and the hyperbolic structure as the point tends to the boundary. In the complex dynamics, we find new phenomenon on the structure of invariant sets near indifferent fixed points. A progress on the boundary Harnack principle on singular domains is done and some estimates about hyperbolic metrics with cone singularities are obtained.

  9. Geometric structure and combinatorial structure of 3-dimensional manifolds

    SAKUMA MAKOTO, SHIMADA Ichiro, DOI Hideo, YASUI Koichi, HIRANOUCHI Toshiro, KAMADA Seiichi, KONO Masaharu, NIKKUNI Ryo, AKIYOSHI Hirotaka, HIRASAWA Mikami, OHSHIKA Ken'ICHI, WADA Masaaki, MIYACHI Hideki, KIN Eiko, KOBAYASHI Tsuyoshi, YAMASHITA Yasushi, MORIMOTO Kanji, NAKANISHI Toshihiro, KOMORI Yohei, SUGAWA Toshiyuki, SHACKLETON Kenneth

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Hiroshima University

    2010/04/01 - 2015/03/31

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    (1) Joint work with Donghi Lee: We established a variation of McShane’s identity for 2-bridge links. Moreover, we introduced the Heckoid orbifolds and proved that they are hyperbolic, and gave a systematic construction of epimorphisms from 2-bridge link groups onto Heckoid groups. Furthermore, we proved that these are the only upper-meridian pair preserving epimorphisms onto even Heckoid groups. (2) Joint work with Ken’ichi Ohshika: We proved that for a Heegarrd surface S of a 3-manifold M with high Hempel distance, a certain natural mapping class group associated with S has a natural free decomposition. We also proved that if S is of bounded combinatorics then there is a nonempty open set U of the projective measured lamination space of S, such that any simple loop in U is not null-homntopic in M and that any two distinct simple loops in U are not homotopic in M.

  10. Various aspects on the study of Geometric Function Theory

    SUGAWA Toshiyuki, SHIGA Hiroshige, YANAGIHARA Hiroshi, SAKAN Ken-ichi, MATSUZAKI Katsuhiko, FUJIKAWA Ege, MIZUTA Yoshihiro, TANIGUCHI Masahiko, FUJIWARA Koji, ABE Makoto

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2010/04/01 - 2015/03/31

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    Geometric Function Theory deals with problems finding relations between geometrically described (simply-connected) domains in the plane and analytic properties of conformal mappings onto them. Bieberbach conjectured that, for a conformal mapping f(z)=a_0+a_1z+a_2z^2+... normalized by a_0=0, a_1=1, the modulus |a_n| of a_n is not greater than n.This conjecture was finally proved by de Branges in his 1985 paper. In the present research project, for example, we showed that the set of conformal mappings as above with half-integral coefficients consists of exactly 21 functions. The similar set for the integral coefficients was previously known to consist of 9 functions.

  11. Ergodic-theoretical study of dynamical systems and stochastic processes related to the theory of Teichmuller spaces

    MORITA Takehiko, SUGITA Hiroshi, OHSHIKA Ken'ichi, SUMI Hiroki, MIYACHI Hideki, ISOZAKI Yasuki, NAKADA Hitoshi, YURI Michiko, TSUJII Masato, SUGAWA Toshiyuki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Osaka University

    2010/04/01 - 2014/03/31

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    For the candidate of the "Teichmuller Brownian motion" obtained in our preceding research, we show that its transition probability densities satisfy some useful inequalities. Unfortunately, we are not so successful that we can establish the explicit relation of its intrinsic metric with the Teichmuller metric. On the other hand, for the renormalized Ruazy-Veech-Zorich induction, we obtain a result that illustrates the validity of Chebotarev type density theorem for the distribution of hyperbolic elements of the mapping class group.

  12. Teichmuller spaces of symmetric structures and the rigidity and fixed-point problems of quasiconformal mapping class groups

    MATSUZAKI Katsuhiko, TANIGUCHI Masahiko, SUGAWA Toshiyuki, SAKAN Kenichi, SHIGA Hiroshige, NAKANISHI Toshihiro, MIYACHI Hideki, ITO Kentaro, FUJIKAWA Ege

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    2008 - 2012

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    We define various classes for self-homeomorphisms of the unit circle from a viewpoint of their quasiconformal extension, and study the parameter spaces of those families, which are regarded as Teichmuller spaces. In particular, for the Teichmuller space of symmetric homeomorphisms, we consider conditions for a group acting on this space to have a fixed point in it. As an application, we give a condition for a group of diffeomorphisms to be conjugate to the canonical group action of the circle (Mobius transformations) as well as a condition for the deformation of such a group to be trivial (that is, to have rigidity).

  13. Research on potential problems from various aspects

    AIKAWA Hiroaki, SHIGA Hiroshige, KIGAMI Jun, TONEGAWA Yoshihiro, HIRATA Kentaro, UENO Kohei, SUZUKI Noriaki, KUMAGAI Takashi, SUGAWA Toshiyuki, SHIMOMURA Tetsu, MURATA Minoru, TADOKORO Yuki, KATAGATA Koh, OHONO Takao

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (A)

    Institution: Hokkaido University

    2008 - 2012

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    Problems on important functions such as (super, sub)harmonic functions appearing in analysis, geometry and probability are referred to as potential problems. We have investigated potential problems from various view points and unveiled deep properties of important functions in connections with nonsmooth domains, fractals, manifolds and functions spaces.

  14. Indiscrete representations of discrete groups

    MAKOTO Sakuma, SEIICHI Kamada, MASAKAZU Teragaito, KEN. ICHI Ohshika, TOSHIYUKI Sugawa, YASUSHI Yamashita, HIROTAKA Akiyoshi, HIROKI Sumi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Challenging Exploratory Research

    Institution: Hiroshima University

    2009 - 2011

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    We completely determined those simple loops on the 2-bridge spheres of 2-bridge links to be null-homotopic or peripheral in the link complements. We also completely determined when two simple loops on the 2-bridge spheres of 2-bridge links to be homotopic in the link complements. As an application of these results, we established a variation of McShane' s identity for 2-bridge links, which gives a formula to express the modulus of the cusp of a 2-bridge link in terms of the complex translation lengths of closed geodesics

  15. Global construction of pleating coordinates of Teichmuller spaces and its applications

    KOMORI Yohei, IMAYOSHI Yoichi, SAKAN Kenichi, SAKUMA Makoto, SUGAWA Toshiyuki, MIYACHI Hideki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Osaka City University

    2007 - 2010

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    We estimate the Teichmuller distance between Riemann surfaces X and Y which is obtained from X byθ-grafting along a simple closed geodesic C. As anapplication we estimate the Teichmuller distance between the conformal boundary andthe convex core boundary of some regular b-groups of type (1,1) one of which gives acounterexample of K=2 conjecture. Also by means of geodesic length functions, werealize Teichmuller spaces of dimension 2 and 3 as convex polyhedron in real projective spaces.

  16. Ergodic-theoretical study of dynamical systems and stochastic processes on moduli space of curves

    MORITA Takehiko, SUGITA Hiroshi, ISOZAKI Yasuki, YOSHINO Masafumi, MATSUMOTO Makoto, IWATA Koichiro, KAWASHITA Mishio, TAKIMOTO Kazuhiro, SUGAWA Toshiyuki, NAKADA Hitoshi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Hiroshima University

    2007 - 2009

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    In 2007, we extended a local central limit theorem for renormalized Rauzy-Veech-Zorichinductions to a wider class of functions than the class in our previous result.from 2008, we started constructing canonical diffusion processes on the teichmuller spaces with Teichmuller metric. In spite of an unexpected difficulty, we fortunately meet a candidate of the "Teichmuller Brownian motion" via Dirichlet space theory.

  17. Loewner方程式の幾何学的函数論および確率過程への応用

    須川 敏幸, 柳原 宏, 盛田 健彦, 吉野 正史, 永井 敏隆, 岩田 耕一郎

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 挑戦的萌芽研究

    Category: 挑戦的萌芽研究

    2007 - 2009

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    本年度は,主に東北大学において幾何学的函数論やLoewner方程式に関するセミナーを学生と一緒に行い,研究を行った.特に,Lawlerによる専門書“Conformally Invariant Processes in the Plane"をテキストに選んでSLEの考察も深めた.一方,分担者の柳原は山口大学,広島大学において幾何学的函数論やポテンシャル論など関連するセミナーに出席するなどして,研究を進めた. 当初はGutlyanskii氏を招聘してLoewner方程式に関する共同研究を再開する予定であったが,氏の多忙により調整が付かず,招聘はかなわなかった.そのかわり,平成22年2月に宮城県大崎市にある東北大学鳴子会館において,SLEやLoewner方程式に関する比較的小規模の勉強会を行った.国内から約30名の参加者が集い,情報交換や知識の共有をはかることができたので,有意義な集会となった. 以上,国内での研究に加え,引き続き韓国においてSeong-A Kim氏らと高次シュワルツ微分やシュワルツ・ピックの補題の精密化など,幾何学的函数論や等角不変量に関する共同研究を行った.また,Yong Chan Kim氏とは,ハーディー空間や単葉函数に関する今日を研究を行った. さらに,6月のCMFT2010集会(アンカラ,トルコ),8月の複素解析国際会議(トゥルク,フィンランド),11月のCMRIF集会(ナウェンチュフ,ポーランド)に招かれ,研究成果について講演を行った.

  18. Research on deformations of real and complex manifolds and variations of invariants

    SHIGA Hiroshige, AIKAWA Hiroaki, SUGAWA Toshiyuki, MURATA Minoru, MATSUZAKI Katsuhiko, NOGUCHI Junjiro, MIYAJIMA Kimio, IMAYOSHI Yoichi, SHISHIKURA Mitsuhiro, SUMI Hiroki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (A)

    Institution: Tokyo Institute of Technology

    2005 - 2008

  19. New development of geometric function theory focused on conformal invariants

    SUGAWA Toshiyuki, MIZUTA Yoshihiro, SAKAN Ken-ichi, SHIBA Masakazu, YOSHINO Masafumi, TANIGUCHI Masahiko, SHIGA Hiroshige, MATSUZAKI Katsuhiko, NAKAHISNI Toshihiro, SHIMOMURA Tetsu

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Category: Grant-in-Aid for Scientific Research (B)

    2005 - 2008

  20. Researches on quasiconformal groups and the modular group of the universal Teichmuller space

    MATSUZAKI Katsuhiko, TANIGUCHI Masahiko, NAKANISHI Toshihiro, SHIGA Hiroshige, SUGAWA Toshiyuki, SAKAN Kenichi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    2004 - 2007

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    The Teichmuller Tare is a deformation space of the conformal structures of a Riemann surface. The quasiconformal mapping class group is a certain quotient group of the quasiconformal homeomorphisms of the Riemann surface and it acts on the Teichmuller space as the group of biholomorphic automorphisms (modular transformations). When Teichmuller spaces are finite dimensional, they are widely studied with great importance in various fields of mathirnatics. We aim to extend them to infinite dimensional Teichmuller sperms. In this research, we investigated the dynamics of the quasiconformal mapping class on the Teichmuller space. For this purpose, we also considered a certain quotient space of the Teichmuller space, which is called the asymptotic Teichmuller space. We first investigated the recurrent set for the mapping class group and proved that the periodic points are not dense in this set. This result was a foundation of our further studies on the action of elliptic modular transformation (conformal mapping classes) and the classification of the modular transformations. Our classification was based on the behavior of the orbit and we specified two classes, which have a similar nature of the modular transformations of finite dimensional Teichmuller spaces. One is a class of stationary mapping classes, and the other is a class of modular transformations that have a fixed point on the asymptotic Teichmuller space. We noticed that the action of a stationary mapping class group is stable, but also gave an example of a non-stationary mapping class group that acts discontinuously. As an extreme case, we dealt with a mapping class group that has a common fixed point on the asymptotic Teichmuller space and proved that such a group consists of countably many elements. As another topic, we studied holomorphic self-covering of Riemann surfaces. We gave a necessary condition for a hyperbolic Riemann surface to admit a (non-injective) holomorphic self-cover in terms of the corresponding Fuchisian group. Namely, if the Fuchsian group is of divergence type at the critical exponent of its Poincare series, then the Riemann surface has no self-covers. The proof used uniqueness of the Patterson-Sullivan measure and can be extended to higher dimensional cases. A holomorphic self-cover of a Riemann surface induces a non-surjective holomorphic self-embedding of its Teichmuller space. We investigated the dynamics of such a self-embedding and examined the distribution of isometric tangent vectors over Teichmuller space. We also extended our observation to quasiregular self-covers of Riemann surfaces.

  21. タイヒミュラー空間上のブラウン運動と曲線のモジュライ空間の確率解析

    盛田 健彦, 岩田 耕一郎, 川下 美潮, 須川 敏幸

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 萌芽研究

    Institution: 広島大学

    2004 - 2006

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    本研究全体を通して,種数2以上のタイヒミュラー計量(T-計量)によるブラウン運動(T-BM)とヴェイユ・ピーターソン計量(WP-計量)によるブラウン運動(WP-BM)のポテンシャル論的な比較を行うことが重要な目標となっている.種数1の場合には,タイヒミュラー空間は複素上半平面とみなされ,写像類群の作用はモジュラー群の作用であって,連分数変換の2回合成というただ一つ力学系の作用と軌道同値となっており,モジュラー曲面上のブラウン運動に関するポテンシャル論的性質と,測地流のエルゴード理論的性質には関連性があることも知られている.前年度(平成17年度)に引き続き,Rauzy inductionを繰り込んで得られる力学系に対して,そのエルゴード理論的挙動を調べた.既に得られている「あるクラスの繰り込まれたRauzy inductionは自然な不変測度に関してBernoulli的であり,滑らかな観測量に関しては相関係数が指数的に減衰するのみならず,常に漸近分散が正となり,非退化な中心極限定理が成立する」という結果の精密化とアーベル微分のモジュライ空間に制限したタイヒミュラー測地流がRauzy inductionの懸垂流として表現されるという事実を組み合わせることによって対応するT-BMに如何なるポテンシャル論的性質が期待できるかを検討した.また,写像類群上のランダムウォークのにDonskerの不変原理を適用してT-BMを構成する方法についても検討した.WP-BMとT-BMのポテンシャル論的な比較については十分な議論ができなかったがBufetov氏によって最近得られた繰り込まれたRauzy inductionの一種であるRauzy-Veech-Zorich inductionに関する評価を応用することによって17年度に得られた上述の結果の精密化には到達できた.

  22. Ergodic-theoretical study of the distribution of Teichmuller closed geodesics and the dynamical zeta functions

    MORITA Takehiko, YOSHINO Masafumi, MATSUMOTO Makoto, KAWASHITA Mishio, SUGAWA Toshiyuki, NAKADA Hitoshi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Hiroshima University

    2004 - 2006

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    We note that the complex upper half-plane, the modular group, the modular surface are regarded as the Teichm011er space, the mapping class group, and the moduli space of curves of genus 1, respectively. Therefore it seems natural to consider the case of genus greater than 1. In the case of genus 1, it is well known that the closed geodesics of modular surface, the conjugacy classes of primitive hyperbolic elements, and the periodic orbits of two-fold iteration of the linear fractional transformations are in the natural one-to-one correspondence and the distribution of closed geodesics satisfies the prime number type theorem. The purpose of this project is to establish the same kind of results for the moduli spaces of hyperbolic curves, especially the prime number type theorem for a restrictive class of Teichmtiller closed geodesics which corresponding to the periodic orbits of the renormalized Rauzy inductions. In 2004, we try to obtain the meromorphic extensions of the dynamical zeta functions of the renormalized Rauzy inductions. We need to establish a systematic way to extend the dynamical zeta functions of hyperbolic dynamics with singularity in sufficiently wide half-plane. To this end we first treat some typical examples to find common structure of those dynamics. As a consequence we obtain a method to extends the zeta function of two-dimensional scattering open billiards without eclipse meromorphically to the domain containing the half-plane consisting of numbers of nonnegative real part by constructing the Lipschitz continuous invariant foliations. In 2005 we generalize the above results of the meromorphic extension obtained in 2004 to a class of Lipschitz continuous Markov systems with Cantor-like invariant sets and establish a way to calculate the special values at the origin for the corresponding dynamical zeta functions. In addition, we also prove the weak type local limit theorem for a class of renormalized Rauzy inductions In 2006, we notice that the recent result obtained by Bufetov can be applied to prove the prime number type theorem for a class of renormalized Rauzy-Veech-Zorich inductions which are interesting but more restrictive class of the renormalized Rauzy inductions. The paper containing the result will be submitted to the appropriate journal in the near future.

  23. 境界の密性がもたらす領域のポテンシャル論的・幾何的性質について

    須川 敏幸

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 若手研究(B)

    Category: 若手研究(B)

    Institution: 広島大学

    2002 - 2004

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    まず,既に京都大学数理解析研究所講究録1293"ポテンシャル論とその周辺"(2002),154-167,に発表済みの「ある密性条件を満たす集合の一般化容量の評価」についてはその後もその後一般距離空間について一般化するなどの改良を加えた上で,英文の論文として現在発表準備中である. また,Seong-A Kim教授との双曲的凸領域の特徴付けに関する共同研究が一旦完了し,その後はリーマン計量を持つリーマン面上の高次の不変微分作用素に関する研究を行い,これまでに知られていた作用素を一般化することに成功した上,驚くべき漸化式を発見するに至った.これについては現在発表準備中である. Yong Chan Kim教授,S.Ponnusamy教授とは単葉函数とシュワルツ微分,双曲幾何,擬等角写像との関連について共同研究を行い,部分的な結果を得た.既にいくつかの論文で結果を発表し,それ以外についても現在論文を投稿中または発表準備中である. Stanislawa Kanas教授とは単位円板から楕円の内部への等角写像について共同研究を行い,懸案であった係数の正値性予想を解決した(現在論文投稿中).またさらに,現在は強凸状函数の強星状性について微分従属式の理論を使って研究を行った(現在発表準備中). Matti Vuorinen教授とは平面領域の双曲計量,またより一般に錐特異性を持つ双曲計量についての共同研究を行った.領域の境界点の様子を用いて双曲密度や双曲距離を評価することに成功した論文が最近Mathematische Zeitschriftに受理されたほか,もう1編を投稿準備中である.

  24. Dynamics of modular groups on infinite dimensional Teichmuller spaces

    MATSUZAKI Katsuhiko, SUGAWA Toshiyuki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Ochanomizu University

    2002 - 2003

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    Teichmueller spaces are not homogeneous spaces and their mudular groups do not act transitively. For compact Riemann surfaces, modular groups act discontinuously, but this is not the case for infinite dimensional Teichmueller spaces. We study the moduli spaces of Riemann surafces of infinite type by considering the chaotic behavior of the action of modular groups. For a viewpoint of general topology, the moduli space is either metrizable or not of the first separation axiom. However, except for a singular part, it can possess a certain geometric structure. In this research, we characterize this stable region by hyperbolic geometric structure of a Riemann surface and construct a contracted moduli space by the completion of the stable region. Consequently, we can describe the closure of a point set in terms of the geomery of Riemann surfaces, which is a point of teh contracted module space. We considered the space of pre-Schwarzian derivatives of univalent functions on the unit disk which extends to quasiconformal mappings of the extended plane in order to investigate the relation between connected components of the pre-Schwarzian derivatives of univalent functions on the unit disk which extends to quasiconformal mappings of the extended plane in order to investigate the relation between connected components of the pre-Schwarzian model of the universal Teichmueller space and classical families of univalent functions. We also investigated geometric properties of univalent functions with a prescribed growth of the Schwarzian derivative and found that they are starlike or convex according to the distance to the origin in the Bers embedding of the universal Teichmueller space.

  25. Analysis of quasisymmetric functions and Teichmuller space

    SAKAN Ken-ichi, NISHIO Masaharu, IMAYOSHI Yoichi, NAKANISHI Toshihiro, TUGAWA Toshiyuki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Osaka City University

    2001 - 2003

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    The head investigator Sakan published jointly with the foreign joint worker D.Partyka "On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve" and "On Heinz's inequality ". In the former paper they introduced, with no use of quasiconformal mappings, some pseudo-metrics into the space of generalized quasisymmetric automorphisms of a Jordan curve, and discussed some applications to topological properties of the Teichmiuller pseudo-metric. In the latter paper they generalized the Heinz's result on one-to-one harmonic mappings F of the unit disc onto itself in the case where F is the Poisson integral of a sense-preserving homeomorphic self-mapping of the unit circle. As an application they inferred a version of Heinz's inequality for harmonic and quasiconformal self-mappings of the unit disc. In a paper to be. submitted, they show an asymptotically sharp variant of Heinz's inequality for harmonic and quasiconformal self-mappings of the unit disc. For the analysis of quasisymmetry, it is important to analyze the representations of maximal dilatations and so on in terms of harmonic measure and crossratio. Furthermore, it turned out that boundary dilatations, conjugate functions and Cauchy singular integrals are deeply related to the quasiconformality of harmonic extensions. Sakan has discussed about these analyses, with investigators Nishio and Yoshida from the viewpoint of potential and probability theory. Further, on extremal extensions which are quite related to boundary dilatations Sakan has contacted foreign joint workers Y.Shen, S.Wu and investigators Ohtake and Sugawa. Moreover, Sakan has discussed with investigators Imayoshi, Komori and Nakanishi about the relation of their researches on Teichmuller space and our research project.

  26. リーマン面の双曲幾何と一様完全性

    須川 敏幸

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 奨励研究(A)

    Category: 奨励研究(A)

    Institution: 京都大学

    1999 - 2000

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    Bergman計量の類似で、与えられたリーマン面上の可積分正則二次微分を用いてこれまで知られていない等角不変な等角計量をリーマン面に導入した。 よく知られているように、二乗可積分な正則一次微分(アーベル微分)に比べて可積分正則二次微分は一般的に豊富に存在し、しかもそれはリーマン面の複素構造の変形と密接に結びついていることから、リーマン面の幾何学的性質を深く反映していると考えられる。 例えば、この計量が双曲計量の定数倍で評価できることとは、可積分正則二次微分が常に双曲的有界になることと同値であることが分かる。 この計量と、Bergman計量、Hahn計量、双曲計量とを比較して、リーマン面における様々な評価を行った。その結果として、この計量がHahn計量と比較可能であることが、実はリーマン面が有界幾何を持つ(つまり、平面領域の場合は境界が一様完全)であることと同値であることが証明できた。 これについては現在論文を投稿中である。 そのほかにも、普偏Teichmuller空間や、単葉関数の挙動についてなど、幅広い研究を行った。

  27. Geometry of webs, Hamiltonian systems and complex dynamics

    NAKAI Isao, SATO Hajime, YOSHINO Masatomi, SUWA Tatsuo, MATSUMOTO Shigenori, KIKKAWA Michihika

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B).

    1998 - 2000

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    We defined a canonical affine connection for integrable first order partial differential equations of finite type, and investigated its singularities along the locus where the foliation structure of solutions degenerates. We proved there exists one to one correspondence of the moduli space of equations and the space of curvature forms in some cases. We proved also the triangulability of the mapping cylinder of generic smooth mappings of manifolds. As an application we proved a naturality formula of the stiefel-homology functor of constructible functions on manifolds to homology classes.

  28. Various quasiconformal extensions of a quasisymmetric automorphism of the unit circle and Teichmuller space

    SAKAN Kenichi, KOMORI Yohei, NISHIO Masaharu, IMAYOSHI Masaharu, NAKANISHI Toshihiro, SUGAWA Toshiyuki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Osaka City University

    1998 - 1999

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    1. The head investigator Sakan obtained jointly with Partyka and Zajac the following results in three published paper. (1) They gave necessary and sufficient conditions on sense-preserving homeomorphisms of the unit circle for the quasiconformality of their harmonic extensions. In particular, the case where the harmonic extension is not quasiconformal was studied. In consequence, suitable examples were constructed. (2) Suppose that the harmonic extension of a sense-preserving homeomorphism of the unit circle is quasiconformal. All such homeomorphisms with a bounded derivative were well characterized. In consequence, a generalization of Martio's result was obtained. (3) By the use of the extension operators, a unified summary on harmonic and quasiconformal extensions was given. 2. Sakan and an investigator Sugawa attended the 12th Conference on Analytic Functions (August30〜September 5, 1998 at Lublin, Poland) and gave lectures. The papers of the results were published. Sakan expressed the Beurling-Ahlfors condition on quasisymmetry in terms of harmonic measure and cross ration. In consequence, Sakan introduced a generalized conformally invariant dilatation on quasisymmetry and discussed its properties. By an application of holomorphic families of univalent functions, Sugawa obtained some results on quasiconformal extendability of univalent functions. 3. Sakan attended the Second ISAAC Conference (August 16〜21, 1999 at Fukuoka Institute of Technology) and Korea-Japan Seminar on Complex Analysis (October 18〜20, 1999 at Yeungnam University, Korea) and gave lectures. The result will soon appear in the Proceedings. On the space of all quasisymmetric automorphisms of a given Jordan curve, a conformally invariant pseudo-metric which is equivalent to the Teichmuller pseudo-metric was introduced with no use of quasiconformal extensions.

  29. Teichmuller空間の境界の幾何学

    須川 敏幸

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 奨励研究(A)

    Category: 奨励研究(A)

    Institution: 京都大学

    1997 - 1998

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    1. 普遍タイヒミュラー空間の前Schwarz微分モデルの構造の解析。 Yong Chan Kim氏との共同研究により、前Schwarz微分のノルムからタイヒミュラー空間の点を表現する単葉函数の増大度評価や計数評価などがどのように得られるかを 明らかにした(プレプリント)。2. (1,1)型タイヒミュラー空間のBers埋め込みのグラフィック化。 大阪市大の小森洋平氏との共同研究により、(1,1)型リーマン面のタイヒミュラー空間のBersモデルの境界をコンピュータにより描画するための実行可能な計算原理を見いだした。実際にはある種の有理函数を係数に持つ微分方程式のモノドロミーを計算し、それを用いてBers埋め込みの境界を知るという方法であり、これまでにこのような計算例は報告されていない。今後はこれをプログラムに乗せて計算を実行させる積もりである。 3. Laplacianに関するDirichlet問題の解の境界正則性の研究。 かなり緩やかな仮定の下で平面領域がLaplacianに関するDirichlet問題についてある指数以下のヘルダー連続性を保存するという結果を示した。例えば、境界が一様完全であればこの結果は正しく、全不連結な境界についてはこれまでこの種の結果は知られていなかったと思われる。同様に、Green函数の境界挙動についても詳しい評価が得られた(プレプリント)。

  30. Analysis and Applications of Teichmuller space

    TANIGUCHI Masahiko, SUGAWA Toshiyuki, KOKUBU Hiroshi, OKAJI Takashi, NOMURA Takaaki, HIRAI Takeshi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: KYOTO UNIVERSITY

    1996 - 1996

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    The results can be devided into two categories ; those on the Teichmuller spaces and those on objects which provide the Teichmuller spaces. Among oter things, the research on the Teichmuller spaces of infinite dimension is very important. The Head investigator Taniguchi has clarified the fundamental structures of the Teichmuller space of a transcendental entire function, including the relationship between the absence of wandering domains and finite dimensionality of the corresponding Teichmuller space. These results are the coproduct with T.Harada, a graduate student, and very important, for they give a new light for the investigations on the complex dynamics induced by transcendental entire functions as in the cases of rational functions and of Kleinian groups. Also Taniguchi has investigated the coiling property, appeared only in the case of infinite dimension, and proved that the Bloch convergence on the universal Teichmuller space is equivalent to Caratheodory convergence, when we consider points of the universal teichmuller space as fractal sets on the plane. Next, a crucial divice for the Teichmuller theory is a quasiconformal map. Investigator Sugawa has suceeded to give a characterization of the Teichmuller spaces of finite Riemann surfaces without cusps. Sugawa has also given quantative estimate on domain constants related to uniform perfectness. As a consequence, we have interesting estimates of the Hausdorff dimensions of the Julia sets of a complex dynamics, or of the limit set of a Kleinian group.

  31. λ-lemmaによるリーマン面の正則族の研究

    須川 敏幸

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 奨励研究(A)

    Category: 奨励研究(A)

    Institution: 京都大学

    1994 - 1994

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    この研究においては主にλ-lemmaの応用について考察を行った。その結果、以前から懸案であったTeichmuller空間のBers埋め込みに関する次の予想:IntS(Γ)=T(Γ)を特にΓが有限生成純双曲的第2種Fuchs群の場合について証明することが出来た。証明のポイントはIntS(Γ)の元に対応する領域を擬等角写像を用いて変形することにあるが、その時にT(Γ)に入らないとすると矛盾が出ることを示すのにIntS(Γ)の(局所)擬等角等質性が用いられ、その部分でλ-lemmaが本質的に用いられる。この証明はGehringによって既に証明されていた最も単純な場合:Γ=1の結果の別証明にもなっている。直観的には擬等角写像を用いた変形の方が分かりやすいように筆者には思われる。(この結果は“On the space of schlicht projective structures on compact Riemann surfaces with boundary"というタイトルで現在投稿中である。) なお、当初の目標であったより一般のリーマン面の正則族についてはまだ研究の緒についたばかりでまだそれほど重要な結果は得られていないが、上記の研究の副産物として双曲的平面領域の解析的普遍被覆写像のSchwarz微分の双曲的ノルムが有限であるという性質と“uniformly perfect"という性質との間に著しい関係があることを見いだした。これらの性質の同値性については既にPommerenkeが指摘しているが、筆者はより精密に定量的な評価を与えることに成功した。

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