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Geometric application of concentration of measure phenomenon

Research Project

Project/Area Number 23840020
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKyoto University

Principal Investigator

FUNANO Kei  京都大学, 大学院・理学研究科, 助教 (40614144)

Co-Investigator(Renkei-kenkyūsha) SHIOYA Takashi  東北大学, 大学院・理学研究科, 教授 (90235507)
Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords測度の集中 / ラプラシアン / リーマン多様体 / 多様体の収束 / Laplacianの固有値 / Ricci曲率 / 測度距離空間 / 曲率次元条件
Research Abstract

We studied properties of eigenavalues of Laplacian on closed Riemannian manifolds of nonnegative Ricci curvature. One of our achievements is the k-th non-trivial eigenvalue of Laplacian on such manifolds is bounded by the first eigenvalue times universal constant depending only on k. In our proof, we obtained a stability result of curvature-dimension condition under concentration topology. This result extends the known-result that cuvature-dimension condition is stable under the measured Gromov-Hausdorff topology.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • Research Products

    (31 results)

All 2013 2012 2011 Other

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (27 results) (of which Invited: 3 results) Remarks (2 results)

  • [Journal Article] Concentration, Ricci curvature, and eigenvalues of Laplacian2013

    • Author(s)
      Kei Funano and Takashi Shioya
    • Journal Title

      Geom. Funct. Anal.

      Volume: 23 Issue: 3 Pages: 888-936

    • DOI

      10.1007/s00039-013-0215-x

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two infinite versions of the nonlinear Dvoretzky theorem2012

    • Author(s)
      Kei Funano
    • Journal Title

      Pacific J. Math

      Volume: 259 Issue: 1 Pages: 101-108

    • DOI

      10.2140/pjm.2012.259.101

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Concentration, separation,and eigenavlues of Laplacian2013

    • Author(s)
      船野敬
    • Organizer
      Connections for Women on theconcentration of measure phenomenon
    • Place of Presentation
      名古屋大学
    • Year and Date
      2013-03-06
    • Related Report
      2012 Final Research Report
  • [Presentation] ラプラシアンの固有値の間の数値的普遍不等式について2013

    • Author(s)
      船野敬
    • Organizer
      リーマン幾何と幾何解析
    • Place of Presentation
      筑波大学
    • Year and Date
      2013-02-22
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Concentration, separation,and eigenvalues2013

    • Author(s)
      船野敬
    • Organizer
      Sturm seminar
    • Place of Presentation
      Bonn university
    • Year and Date
      2013-01-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Concentration, separation, and eigenvalues of Laplacian2013

    • Author(s)
      船野敬
    • Organizer
      Connections for Women on the concentration of measure phenomenon
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 測度集中とラプラシアン2012

    • Author(s)
      船野敬
    • Organizer
      談話会
    • Place of Presentation
      京都大学
    • Year and Date
      2012-12-19
    • Related Report
      2012 Final Research Report
  • [Presentation] 無限版とlp 版非線形ドボレツキーの定理について2012

    • Author(s)
      船野敬
    • Organizer
      多様体の微分方程式
    • Place of Presentation
      金沢大学
    • Year and Date
      2012-11-15
    • Related Report
      2012 Final Research Report
  • [Presentation] 無限版とlp 版非線形ドボレツキーの定理について2012

    • Author(s)
      船野敬
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村南阿蘇(熊本県阿蘇郡)
    • Year and Date
      2012-09-25
    • Related Report
      2012 Final Research Report
  • [Presentation] 無限版非線形ドボレツキーの定理について2012

    • Author(s)
      船野敬
    • Organizer
      幾何学シンポジウム
    • Place of Presentation
      九州大学
    • Year and Date
      2012-08-27
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] 無限版とlp 版非線形ドボレツキーの定理について2012

    • Author(s)
      船野敬
    • Organizer
      剛性セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2012-06-08
    • Related Report
      2012 Final Research Report
  • [Presentation] Infinite and lp versions ofnonlinear Dvoretzky's theorem2012

    • Author(s)
      船野敬
    • Organizer
      Groupactions and K-theory
    • Place of Presentation
      京都大学
    • Year and Date
      2012-03-14
    • Related Report
      2012 Final Research Report
  • [Presentation] Infinite and $¥ell_p$ versions of nonlinear Dvoretzky's theorem2012

    • Author(s)
      船野敬
    • Organizer
      Group actions and K-theory
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2012-03-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] 無限版非線形ドボレツキーの定理について2012

    • Author(s)
      船野敬
    • Organizer
      測地線及び関連する諸問題
    • Place of Presentation
      熊本大学(招待講演)
    • Year and Date
      2012-01-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] 無限版非線形ドボレツキ-の定理について2012

    • Author(s)
      船野敬
    • Organizer
      測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2012-01-08
    • Related Report
      2012 Final Research Report
  • [Presentation] 無限版とl_p版非線形ドボレツキーの定理について2012

    • Author(s)
      船野敬
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村南阿蘇
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 無限版とl_p版非線形ドボレツキーの定理について2012

    • Author(s)
      船野敬
    • Organizer
      多様体の微分方程式
    • Place of Presentation
      金沢大学サテライトプラザ
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Some infinite versions ofnonlinear Dvoretzky's theorem2011

    • Author(s)
      船野敬
    • Organizer
      Doctorial Forum of Mathematics betweenFudan and Kyoto Universities
    • Place of Presentation
      復旦大学
    • Year and Date
      2011-11-03
    • Related Report
      2012 Final Research Report
  • [Presentation] Some infinite versions of nonlinear Dvoretzky's theorem2011

    • Author(s)
      船野敬
    • Organizer
      Doctorial Forum of Mathematics between Fudan and Kyoto Universities
    • Place of Presentation
      Fundan university(中国)(招待講演)
    • Year and Date
      2011-11-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] Concentration of measurephenomenon and eigenvalues ofLaplacian2011

    • Author(s)
      船野敬
    • Organizer
      5th InternationalConference on Stochastic Analysis andits Applications
    • Place of Presentation
      Bonn university
    • Year and Date
      2011-09-06
    • Related Report
      2012 Final Research Report
  • [Presentation] Concentration of measure phenomenon and eigenvalues of Laplacian2011

    • Author(s)
      船野敬
    • Organizer
      5th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      Hausdorff center for mathematics(ドイツ)
    • Year and Date
      2011-09-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] 測度の集中現象とラプラシアンの固有値の挙動2011

    • Author(s)
      船野敬
    • Organizer
      東京確率論セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2011-07-04
    • Related Report
      2012 Final Research Report
  • [Presentation] 測度の集中現象とラプラシアンの固有値の挙動2011

    • Author(s)
      船野敬
    • Organizer
      東京確率論セミナー
    • Place of Presentation
      東京工業大学(招待講演)
    • Year and Date
      2011-07-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Concentration, convergence,and eigenvalues of Laplacian2011

    • Author(s)
      船野敬
    • Organizer
      GCOE teatime
    • Place of Presentation
      京都大学
    • Year and Date
      2011-06-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Concentration, convergence, and eigenvalues of Laplacian2011

    • Author(s)
      船野敬
    • Organizer
      GCOE tea time
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2011-06-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] 測度の集中現象とラプラシアンの固有値の挙動2011

    • Author(s)
      船野敬
    • Organizer
      九州大学幾何学セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2011-06-03
    • Related Report
      2012 Final Research Report
  • [Presentation] 測度の集中現象とラプラシアンの固有値の挙動2011

    • Author(s)
      船野敬
    • Organizer
      幾何学セミナー
    • Place of Presentation
      九州大学(招待講演)
    • Year and Date
      2011-06-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] S.Y.Cheng による定理の一般化について2011

    • Author(s)
      船野敬
    • Organizer
      微分トポロジーセミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2011-04-12
    • Related Report
      2012 Final Research Report
  • [Presentation] S.Y.Chengによる定理の一般化について2011

    • Author(s)
      船野敬
    • Organizer
      微分トポロジーセミナー
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2011-04-12
    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      https://sites.google.com/site/keifunanoshomepage/

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      https://sites.google.com/site/keifunanoshomepage/

    • Related Report
      2011 Annual Research Report

URL: 

Published: 2011-09-05   Modified: 2019-07-29  

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