Research on geometry involving Ricci flow

• Project/Area Number: 26800035
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: Yokota Takumi 京都大学, 数理解析研究所, 助教 (70583855)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: CAT(1)-空間 / リッチ流

Outline of Final Research Achievements

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.

Research Products

• [Journal Article] Law of large numbers in CAT(1)-spaces of small radii (2018)
  • Author(s): Yokota Takumi
  • Journal Title: Calculus of Variations and Partial Differential Equations Volume: 57 Issue: 2
  • DOI: 10.1007/s00526-018-1310-5
  • Peer Reviewed
• [Journal Article] Convex functions and $p$-barycenter on CAT(1)-spaces of small radii (2017)
  • Author(s): Takumi Yokota
  • Journal Title: Tsukuba Journal of Mathematics Volume: 印刷中
  • Peer Reviewed
• [Presentation] Stability of RCD condition under concentration topology (2018)
  • Author(s): 横田巧
  • Organizer: 測地線及び関連する諸問題
  • Invited
• [Presentation] Stability of RCD condition under concentration topology (2018)
  • Author(s): Takumi Yokota
  • Organizer: 確率論と幾何学
  • Int'l Joint Research / Invited
• [Presentation] Stability of RCD condition under concentration topology (2018)
  • Author(s): 横田巧
  • Organizer: リーマン幾何と幾何解析
• [Presentation] Law of large numbers in CAT(1)-spaces of small radii (2017)
  • Author(s): 横田巧
  • Organizer: リーマン幾何と幾何解析
  • Place of Presentation: 京都大学（京都府京都市）
  • Year and Date: 2017-02-24
• [Presentation] Barycenter of probability measures on CAT(1)-spaces of small radii (2017)
  • Author(s): Takumi Yokota
  • Organizer: KTGU Mathematics Workshop for Young Researchers
  • Place of Presentation: 京都大学（京都府京都市）
  • Year and Date: 2017-02-20
  • Int'l Joint Research / Invited
• [Presentation] Law of large numbers in CAT(1)-spaces of small radii (2017)
  • Author(s): 横田巧
  • Organizer: 測地線および関連する諸問題
  • Place of Presentation: 熊本大学（熊本県熊本市）
  • Year and Date: 2017-01-07
  • Invited
• [Presentation] Convex functions and $p$-barycenter on CAT(1)-spaces of small radii (2016)
  • Author(s): 横田巧
  • Organizer: 福岡大学微分幾何研究会
  • Place of Presentation: 福岡大学セミナーハウス（福岡県福岡市）
  • Year and Date: 2016-11-03
  • Invited
• [Presentation] 半径の小さいCAT(1)-空間上の凸関数と確率測度のp-重心 (2016)
  • Author(s): 横田巧
  • Organizer: 日本数学会2016年度秋季総合分科会
  • Place of Presentation: 関西大学（大阪府吹田市）
  • Year and Date: 2016-09-15
• [Presentation] Open problems on Ricci flow (2016)
  • Author(s): 横田巧
  • Organizer: Geometric flows and related problems
  • Place of Presentation: 東京工業大学（東京都・目黒区）
  • Year and Date: 2016-03-04
  • Invited
• [Presentation] Convex functions and p-barycenter on CAT(1)-spaces of small radii (2016)
  • Author(s): Takumi Yokota
  • Organizer: Metric Geometry and Its Applications
  • Place of Presentation: 上海（中華人民共和国）
  • Year and Date: 2016-02-24
  • Int'l Joint Research / Invited
• [Presentation] Convex functions and p-barycenter on CAT(1)-spaces of small radii (2016)
  • Author(s): 横田巧
  • Organizer: 測地線及び関連する諸問題
  • Place of Presentation: 熊本大学（熊本県・熊本市）
  • Year and Date: 2016-01-10
  • Invited
• [Presentation] リッチ流の曲率がピンチされた完備な古代解について (2015)
  • Author(s): 横田巧
  • Organizer: 測地線及び関連する諸問題
  • Place of Presentation: 熊本大学
  • Year and Date: 2015-01-10
  • Invited
• [Presentation] Complete ancient solutions to the Ricci flow with pinched curvature (2014)
  • Author(s): Takumi Yokota
  • Organizer: 低次元多様体モジュライ空間の幾何学
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-12-08
  • Invited
• [Presentation] 半径の小さいCAT(1)-空間上の確率測度の重心 (2014)
  • Author(s): 横田巧
  • Organizer: 日本数学会2014年度秋季総合分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-26
  • Invited
• [Presentation] Convex functions and barycenter on CAT(1)-spaces of small radii (2014)
  • Author(s): Takumi Yokota
  • Organizer: 確率論と幾何学
  • Place of Presentation: 東京工業大学
  • Year and Date: 2014-09-23
  • Invited
• [Presentation] リッチ流の曲率がピンチされた完備な古代解について (2014)
  • Author(s): 横田巧
  • Organizer: 第61回幾何学シンポジウム
  • Place of Presentation: 名城大学
  • Year and Date: 2014-08-26
  • Invited
• [Remarks] Yokota Takumi's Website
  • URL: http://www.kurims.kyoto-u.ac.jp/~takumiy/