Details of the Researcher

PHOTO

Takumi Yokota
Section
Graduate School of Science
Job title
Associate Professor
Degree

  • Ph.D. (Mathematics)

Professional Memberships 1

  • 日本数学会

Research Areas 1

  • Natural sciences / Geometry /

Papers 14

  1. Boundedness of precompact sets of metric measure spaces

    Daisuke Kazukawa, Takumi Yokota

    Geometriae Dedicata　215　(1)　229-242　2021/12/01

    Publisher: Springer Science and Business Media B.V.

    DOI： 10.1007/s10711-021-00646-7 　

    ISSN： 1572-9168 0046-5755

  2. Law of large numbers in CAT(1)-spaces of small radii Peer-reviewed

    Takumi Yokota

    Calculus of Variations and Partial Differential Equations　57　(2)　2018/04/01

    Publisher: Springer New York LLC

    DOI： 10.1007/s00526-018-1310-5 　

    ISSN： 0944-2669

  3. Convex functions and $p$-barycenter on CAT(1)-spaces of small radii Peer-reviewed

    Takumi Yokota

    Tsukuba Journal of Mathematics　41　(1)　43-80　2017

  4. Complete ancient solutions to the Ricci flow with pinched curvature Peer-reviewed

    Takumi Yokota

    COMMUNICATIONS IN ANALYSIS AND GEOMETRY　25　(2)　485-506　2017

    DOI： 10.4310/CAG.2017.v25.n2.a8 　

    ISSN： 1019-8385

    eISSN： 1944-9992

  5. Convex functions and barycenter on CAT(1)-spaces of small radii Peer-reviewed

    Takumi Yokota

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　68　(3)　1297-1323　2016/07

    DOI： 10.2969/jmsj/06831297 　

    ISSN： 0025-5645

  6. On the spread of positively curved Alexandrov spaces Peer-reviewed

    Takumi Yokota

    MATHEMATISCHE ZEITSCHRIFT　277　(1-2)　293-304　2014/06

    DOI： 10.1007/s00209-013-1255-5 　

    ISSN： 0025-5874

    eISSN： 1432-1823

  7. On the filling radius of positively curved Alexandrov spaces Peer-reviewed

    Takumi Yokota

    Mathematische Zeitschrift　273　(1-2)　161-171　2013

    DOI： 10.1007/s00209-012-0999-7 　

    ISSN： 0025-5874 1432-1823

  8. Addendum to 'Perelman's reduced volume and a gap theorem for the Ricci flow' Peer-reviewed

    Takumi Yokota

    COMMUNICATIONS IN ANALYSIS AND GEOMETRY　20　(5)　949-955　2012/12

    DOI： 10.4310/CAG.2012.v20.n5.a2 　

    ISSN： 1019-8385

  9. A rigidity theorem in Alexandrov spaces with lower curvature bound Peer-reviewed

    Takumi Yokota

    MATHEMATISCHE ANNALEN　353　(2)　305-331　2012/06

    DOI： 10.1007/s00208-011-0686-8 　

    ISSN： 0025-5831

  10. CONE STRUCTURE OF L-2-WASSERSTEIN SPACES Peer-reviewed

    Asuka Takatsu, Takumi Yokota

    JOURNAL OF TOPOLOGY AND ANALYSIS　4　(2)　237-253　2012/06

    DOI： 10.1142/S1793525312500112 　

    ISSN： 1793-5253

  11. On the asymptotic reduced volume of the Ricci flow Peer-reviewed

    Takumi Yokota

    ANNALS OF GLOBAL ANALYSIS AND GEOMETRY　37　(3)　263-274　2010/03

    DOI： 10.1007/s10455-009-9184-6 　

    ISSN： 0232-704X

  12. A gap theorem for ancient solutions to the Ricci flow Peer-reviewed

    Takumi Yokota

    PROBABILISTIC APPROACH TO GEOMETRY　57　505-514　2010

  13. Perelman's reduced volume and a gap theorem for the Ricci flow Peer-reviewed

    Takumi Yokota

    Communications in Analysis and Geometry　17　(2)　227-263　2009/03

    ISSN： 1019-8385

  14. Curvature integrals under the Ricci flow on surfaces Peer-reviewed

    Takumi Yokota

    Geometriae Dedicata　133　(1)　169-179　2008/04

    DOI： 10.1007/s10711-008-9241-5 　

    ISSN： 0046-5755

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Research Projects 6

  1. New developments in gradient flow theory on metric 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)

    Institution: Osaka University

    2024/04/01 - 2029/03/31

  2. Geometry of metric measure spaces and pyramids

    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: Tohoku University

    2023/04/01 - 2028/03/31

  3. Geometry of optimal transport theory and gradient flows

    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

    2019/04/01 - 2024/03/31

  4. 曲率が上または下に有界な空間の幾何学

    横田 巧

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(C)

    Institution: 東北大学

    2018/04/01 - 2023/03/31

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    2021年度も引き続き、測度距離空間（metric measure space、mm空間）の幾何学、特に Gromov が測度距離空間の同型類全体の集合に導入したボックス距離とリプシッツ順序に関する研究を行った。前年度からの数川大輔氏（大阪大学）との共同研究では、Gromov が主張し証明の概略のみが与えられていた、測度距離空間の同型類全体の集合においてボックス距離に関する任意の相対コンパクト集合はリプシッツ順序に関して有界である、つまりその相対コンパクト集合に属す任意の測度距離空間よりもリプシッツ順序の意味で大きい測度距離空間が存在するという定理と、その定理の類似の命題として、コンパクト距離空間の等長類全体の集合における Gromov-Hausdorff 距離と測度距離空間の場合と同様に定義されるリプシッツ順序に関する同様の命題の証明を完成させ、論文として投稿し出版された。更に、この定理と命題を相対コンパクト集合がピラミッドと呼ばれる集合に含まれている場合に拡張する定理の証明を目指した。 <BR> また、修士論文を指導した大学院生やポスドクと、測度距離空間の曲率次元条件 CD(K, N) の特に次元 N が負の場合、測度距離空間上の特にバナッハ空間値写像のソボレフ空間、Brouwer の不動点定理の拡張である集合値写像に対する不動点定理、サブリーマン多様体の幾何学などについて、定期的にセミナーを行い議論した。

  5. Research on geometry involving Ricci flow

    Yokota Takumi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Young Scientists (B)

    Institution: Kyoto University

    2014/04/01 - 2018/03/31

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    Several results on the p-barycenter of probability measures on CAT(1)-spaces of small radius were obtained. CAT(1)-spaces are metric spaces of curvature at most 1. In particular, the unique existence and some properties of p-barycenter of probability measures on those spaces were obtained. These are extensions of the results known on CAT(0)-spaces. Moreover, the law of large number formulated with p-barycenter of probability measures on CAT(1)-spaces of small radius was proved.

  6. Comparison geometry of Ricci flow and Ricci solitons

    YOKOTA Takumi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Research Activity Start-up

    Institution: Kyoto University

    2010 - 2011

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    In this research, we mainly studied geometries of the Ricci fow and Alexandrov spaces of curvature bounded below, and we refined our gap theorem for gradient shrinking Ricci solitons, which are self-similar solutions to the Ricci flow equation. We also proved comparison and rigidity theorems stating that the filling radius of any finite-dimensional Alexandrov space with a positive lower curvature bound is at most that of the round sphere, and the equality holds if and only if it is isometric to the round sphere.

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