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博士(数理科学)(東京大学)
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修士(数理科学)(東京大学)
Professional Memberships 1
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Mathematical Society of Japan
Research Interests 7
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harmonic forms
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L^2 Stokes theorem
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elliptic boundary value problem
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collapsing of Riemannian manifolds
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differential forms
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eigenvalues
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Hodge-Laplacian
Research Areas 1
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Natural sciences / Geometry / Differential Geometry
Papers 13
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Small eigenvalues of the rough and Hodge Laplacians under fixed volume Peer-reviewed
Colette Anné, Junya Takahashi
to appear in Ann. Fac. Sci Toulouse 2022
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L2-harmonic forms on incomplete riemannian manifolds with positive Ricci curvature Invited Peer-reviewed
Junya Takahashi
Mathematics 6 (5) 1-11 2018/05/09
Publisher: MDPI AGDOI: 10.3390/math6050075
ISSN:2227-7390
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Partial collapsing and the spectrum of the Hodge-de Rham operator Peer-reviewed
Colette Anné, Junya Takahashi
Analysis & PDE 8 (5) 1025-1050 2015
Publisher: MATHEMATICAL SCIENCE PUBLISSN:1948-206X
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p-spectrum and collapsing of connected sums Peer-reviewed
Colette Anné, Junya Takahashi
Transactions of the American Mathematical Society 364 (4) 1711-1735 2012/04
Publisher: AMER MATHEMATICAL SOCDOI: 10.1090/S0002-9947-2011-05351-1
ISSN:0002-9947
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Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian Peer-reviewed
Junya Takahashi
Manuscripta Mathematica 121 (2) 191-200 2006/10
Publisher: SPRINGERDOI: 10.1007/s00229-006-0035-5
ISSN:0025-2611
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The gap of the eigenvalues for p-forms and harmonic p-forms of constant length Peer-reviewed
Junya Takahashi
Journal of Geometry and Physics 54 (4) 476-484 2005/08
Publisher: ELSEVIER SCIENCE BVDOI: 10.1016/j.geomphys.2004.11.007
ISSN:0393-0440
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms Peer-reviewed
Junya Takahashi
Mathematische Zeitschrift 250 (1) 43-57 2005/05
Publisher: SPRINGERDOI: 10.1007/s00209-004-0735-z
ISSN:0025-5874
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On the gap between the first eigenvalues of the Laplacian on functions and p-forms Peer-reviewed
Junya Takahashi
Annals of Global Analysis and Geometry 23 (1) 13-27 2003/03
ISSN:0232-704X
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Collapsing of connected sums and the eigenvalues of the Laplacian Peer-reviewed
Junya Takahashi
Journal of Geometry and Physics 40 (3-4) 201-208 2002/01
Publisher: ELSEVIER SCIENCE BVISSN:0393-0440
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Small eigenvalues on p-forms for collapsings of the even-dimensional spheres Peer-reviewed
Junya Takahashi
Manuscripta Mathematica 109 (1) 63-71 2002
ISSN:0025-2611
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On the gap between the first eigenvalues of the Laplacian on functions and 1-forms Peer-reviewed
Junya Takahashi
Journal of the Mathematical Society of Japan 53 (2) 307-320 2001/04
Publisher: MATH SOC JAPANISSN:0025-5645
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Upper bounds for the eigenvalues of the Laplacian on forms on certain Riemannian manifolds Peer-reviewed
Junya Takahashi
Journal of the Mathematical Sciences, the University of Tokyo 6 (1) 87-99 1999/01
Publisher: The University of TokyoISSN:1340-5705
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The first eigenvalue of the Laplacian on p-forms and metric deformations Peer-reviewed
Junya Takahashi
Journal of the Mathematical Sciences, the University of Tokyo 5 (2) 333-344 1998/04/01
Publisher: The University of TokyoISSN:1340-5705
Presentations 47
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Small eigenvalues of the Hodge-Laplacian with sectional curvature bouded below Invited
Junya Takahashi
2024/02/21
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Small eigenvalues of the Hodge-Laplacian with sectional curvature bouded below Invited
Junya Takahashi
Global Analysis and Geometry 2023 at Osaka, Osaka Metropolitan Univ. 2023/10/21
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Small eigenvalues of the Hodge-Laplacian with sectional curvature bouded below
Junya Takahashi, Colette Anné
2023/09/22
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Small eigenvalues of the rough and Hodge Laplacians under fixed volume Invited
Junya Takahashi
Geometry and Analysis Seminar -- Mini Workshop 2023, Tohoku Univ. 2023/01/25
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Small eigenvalues of the rough and Hodge Laplacians under fixed volume Invited
Junya Takahashi
2022/06/21
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Small eigenvalues of the rough and Hodge Laplacians under fixed volume
Junya Takahashi, Colette Anné
2022/03/31
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Partial collapsing and the spectrum of the Hodge-Laplacian International-coauthorship Invited
Junya Takahashi
2016/11/19
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Partial collapsing and the spectrum of the Hodge-Laplacian Invited
Junya Takahashi
2014/03/07
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Partial collapsing and the spectrum of the Hodge-Laplacian Invited
Junya Takahashi
2013/10/22
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一般化された連結和の崩壊と Hodge-Laplacian の固有値の収束 Invited
Junya Takahashi
2013/08/25
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Partial collapsing and the spectrum of the Hodge-de Rham operator Invited
Junya Takahashi
Geometry and Probability, Kyoto University 2013/08/08
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Collapsing to Riemannian manifolds to the intervals and the convergence of the eigenvalues of the Laplacian Invited
Junya Takahashi
2006/04/18
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms Invited
Junya Takahashi
International Workshop on Differential Geometry, Saga University 2005/12/24
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Riemann 多様体の崩壊と微分形式の固有値 Invited
高橋淳也
広島幾何学研究集会, 広島大学 2005/10/07
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Collapsing, surgery and the first eigenvalues of the Laplacian on $p$-forms Invited
Junya Takahashi
Geometry and Probability, Tohoku University 2005/09/06
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Riemann 多様体の崩壊と p-form の大きい固有値 Invited
2005/08/20
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Collapsing of Riemannian manifolds and large eigenvalues of the Laplacian on $p$-forms Invited
Junya Takahashi
Kunitachi One-Day Symposium on Geometric Analysis, 一橋大学 2005/07/09
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms in collapsing International-presentation
Junya Takahashi
Séminaire de Géométrie, Université de Nantes, France 2005/05/27
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms in collapsing International-presentation Invited
Junya Takahashi
Analytic aspects of problem in Riemannian geometry, l'Aber Wrac'h, France 2005/05/09
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The gap between the first eigenvalues of the Laplacian on function and p-forms International-presentation
Junya Takahashi
Séminaire de Géométrie, Université de Tours, France 2004/09/10
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The gap between the first eigenvalues of the Laplacian on function and p-forms International-presentation
Junya Takahashi
Séminaire de théorie spectrale et géométrie, Université de Neuchâtel, Suisse 2004/08/24
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms International-presentation
Junya Takahashi
Séminaire de théorie spectrale et géométrie, Université de Neuchâtel, Suisse 2004/08/20
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Small eigenvalues on p-forms of collapsing of the even dimensional spheres International-presentation International-coauthorship
Junya Takahashi
Séminaire de théorie spectrale et géométrie, Université de Neuchâtel, Suisse 2004/08/18
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms Invited
Junya Takahashi
2004/06/29
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崩壊における p-form の大きい固有値とコホモロジー群の消滅 Invited
高橋淳也
微分幾何学火曜セミナー, 筑波大学 2004/06/08
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms Invited
Junya Takahashi
Spectral Geometry, Asymptotic Analysis and Related Topics, Keio University 2004/02/03
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Riemann 多様体の崩壊と微分形式の Laplacian の固有値 Invited
高橋淳也
談話会, 東北大学理学部 2003/12/22
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コホモロジー群の消滅と $p$-form の大きい固有値 Invited
高橋淳也
幾何学セミナー, 九州大学 2003/11/28
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コホモロジー群の消滅と $p$-form の大きい固有値
高橋 淳也
日本数学会幾何学分科会 千葉大学 2003/09/26
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Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms
Junya Takahashi
Probability and Geometric Analysis, Yokohama City University 2003/09/17
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球面の崩壊と $p$-form の Laplacian の固有値 Invited
高橋淳也
談話会, 立教大学 2003/06/16
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球面の崩壊と $p$-form の Laplacian の固有値 Invited
高橋 淳也
情報数理談話会, 東北大学情報科学研究科 2003/06/10
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Riemann 多様体の崩壊と微分形式の Laplacian の第 1 固有値 Invited
高橋 淳也
大岡山談話会,東京工業大学 2003/01/06
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球面の崩壊における小さい固有値と大きい固有値 Invited
高橋淳也
微分幾何学, 九重研究集会 2002/09/14
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偶数次元球面の $p$-form の小さい固有値と gap 問題 Invited
高橋 淳也
第49回幾何学シンポジウム,大阪大学 2002/07/28
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Small eigenvalues on $p$-forms on the even dimensional spheres and the gap problem International-presentation
Junya Takahashi
Second Russian-German Geometry Meeting dedicated to 90-anniversary of A.D. Alexandrov, Euler International Mathematical Institute, Sankt Petersburg, Russia 2002/06/17
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多様体の崩壊と微分形式に作用する Laplacian の第 $1$ 固有値 Invited
高橋淳也
幾何学セミナー, 東北大学 2002/05/07
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偶数次元球面の崩壊における $p$-forms の小さい固有値
高橋淳也
日本数学会幾何学分科会, 明治大学 2002/03/28
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Riemann 多様体の崩壊と微分形式に作用する Laplacian の固有値
高橋淳也
トポロジーセミナー, 東京大学 2002/01/22
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偶数次元球面の崩壊における $p$-form の小さい固有値 Invited
高橋淳也
多様体上の微分方程式, 金沢大学 2001/12/13
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Small eigenvalues on $p$-forms for collapsing of the even dimensional spheres
Junya Takahashi
Geometry and Probability, Tohoku University 2001/11/21
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連結和の崩壊における Laplacian の固有値の収束とその応用 Invited
高橋淳也
微分幾何学火曜セミナー, 筑波大学 2001/10/23
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Collapsing of connected sums and the eigenvalues of the Laplacian
2001/10/04
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連結和の崩壊と Laplacian の固有値の収束 Invited
高橋 淳也
第48回幾何学シンポジウム, 茨城大学 2001/08/28
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連結和の崩壊と Laplacian の固有値の収束 Invited
高橋淳也
幾何学と物理学セミナー, 早稲田大学 2001/06/01
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連結和の崩壊と Laplacian の固有値の収束 Invited
高橋淳也
Lie 群と幾何セミナー, 上智大学 2001/05/16
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連結和の崩壊と Laplacian の固有値の収束 Invited
高橋淳也
微分幾何セミナー, 東京都立大学 2001/04/20
Research Projects 7
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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
Category: Grant-in-Aid for Scientific Research (B)
Institution: Tohoku University
2017/04/01 - 2022/03/31
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特異点の幾何とホッジ・ラプラシアンの固有値の研究
高橋 淳也
System: 基盤研究(C)
Institution: 東北大学
2016/04 - 2021/03
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多様体の崩壊に対するホッジ・ラプラシアンの固有値の極限の研究
高橋 淳也
System: 若手研究(B)
Institution: 東北大学大学院情報科学研究科
2012/04 - 2016/03
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Convergence theory of metric measure spaces and its development
KASUE Atsushi, URAKAWA Hajime, NAYATANI Shin, KATO Shin, KUMURA Hironori, TAKAHASHI Junnya
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: Kanazawa University
2007 - 2009
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微分形式における小さい固有値の位相的性質の研究
高橋 淳也
System: 若手研究(B)
Institution: 東北大学大学院情報科学研究科
2007/04 - 2008/03
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リーマン多様体の崩壊と微分形式のラプラシアンの固有値の研究
高橋 淳也
System: 若手研究(B)
Category: 若手研究(B)
Institution: 東北大学大学院情報科学研究科
2004/04 - 2007/03
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リーマン多様体の崩壊における微分形式のラプラシアンの固有値の研究
高橋 淳也
System: 特別研究員奨励費
Category: 特別研究員奨励費
Institution: 東北大学理学研究科学振特別研究員
2002/04 - 2003/03