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Geometric analysis on asymptotically symmetric spaces and parabolic geometries

Research Project

Project/Area Number 17K14189
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionOsaka University

Principal Investigator

Matsumoto Yoshihiko  大阪大学, 理学研究科, 助教 (00710625)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Discontinued (Fiscal Year 2020)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords微分幾何学 / リーマン幾何学 / アインシュタイン方程式 / 漸近的対称空間 / 共形幾何学 / CR幾何学 / 幾何学 / リーマン幾何 / 放物幾何
Outline of Final Research Achievements

The hyperbolic space, a mathematical concept found in the nineteenth century that opened the door toward modern study of geometry, has been generalized in many ways, and there is a relatively recent generalization called asymptotically symmetric spaces. Of central interest are those spaces satisfying the Einstein equation.
Our aim in this research project was to deliver substantial progress in this field. We proposed that asymptotically symmetric spaces of a certain type be furnished with an additional geometric structure (an almost complex structure satisfying some partial differential equation), and proved a theorem that systematically provides examples of such a furnishment. Moreover, we obtained a new construction of a family of asymptotically symmetric spaces of another type, and studied the interesting limiting behavior of the family.

Academic Significance and Societal Importance of the Research Achievements

本課題で実施した研究は純粋数学に属するもので、近い未来に実用的な意味で社会に役立つことはおそらくない。しかし、人類の共有する知的地平を広げるという点において意義がある。ひいては、国際社会において日本が文化的に敬意をもたれることにも、多少の貢献があるかもしれない。
学術的には、世界的にみて類例のない研究の方向性を示したものと信ずる。この方向性を発展させることができるか、引き続き取り組みを進めていきたい。また、物理学には何らかの形で影響をもたらす可能性があると期待される。

Report

(4 results)
  • 2020 Final Research Report ( PDF )
  • 2019 Annual Research Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (37 results)

All 2020 2019 2018 2017 Other

All Int'l Joint Research (7 results) Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (26 results) (of which Int'l Joint Research: 15 results,  Invited: 20 results) Remarks (2 results)

  • [Int'l Joint Research] Stanford University/Worcester Polytechnic Institute(米国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Stanford University/Princeton University/Worcester Polytechnic Institute(米国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Scuola Normale Superiore(イタリア)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Academia Sinica(その他の国・地域)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Stanford University/Princeton University/Worcester Polytechnic Institute(米国)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Scuola Normale Superiore(イタリア)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Academia Sinica(台湾)

    • Related Report
      2017 Research-status Report
  • [Journal Article] A construction of Poincare-Einstein metrics of cohomogeneity one on the ball2019

    • Author(s)
      Yoshihiko Matsumoto
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 147 Issue: 9 Pages: 3983-3993

    • DOI

      10.1090/proc/14525

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Einstein metrics on strictly pseudoconvex domains from the viewpoint of bulk-boundary correspondence2018

    • Author(s)
      Yoshihiko Matsumoto
    • Journal Title

      Geometric Complex Analysis

      Volume: - Pages: 235-245

    • DOI

      10.1007/978-981-13-1672-2_18

    • ISBN
      9789811316715, 9789811316722
    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] A construction of Poincare-Einstein metrics of cohomogeneity one on the ball2020

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      2020 Taipei-Hsinchu Conference on Geometric Invariance and Partial Differential Equations
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] CR structures, ACH-Einstein fillings, and almost complex structures2020

    • Author(s)
      松本佳彦
    • Organizer
      リーマン幾何と幾何解析
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] CR structures, ACH-Einstein fillings, and almost complex structures2020

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      韓国高等科学院セミナー
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Deformation of Einstein metrics and almost complex structures on strictly pseudoconvex domains2019

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      Differential Geometry & Geometric Analysis Seminar(プリンストン大学)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] GJMS operators, Q-curvature, and obstruction tensor of partially integrable CR manifolds2019

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      アメリカ数学会Spring Eastern Sectional Meeting "Sub-Riemannian and CR geometric analysis"
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Geometric analysis on asymptotically hyperbolic and complex hyperbolic spaces2019

    • Author(s)
      松本佳彦
    • Organizer
      日本数学会秋季総合分科会(幾何学分科会特別講演)
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] CR structures, ACH-Einstein fillings, and almost complex structures2019

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      The first Geometry Conference for Friendship of Japan and Germany
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Canonical almost complex structures on ACH Einstein manifolds2019

    • Author(s)
      松本佳彦
    • Organizer
      複素解析幾何セミナー(東京大学)
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Canonical almost complex structures on ACH Einstein manifolds2019

    • Author(s)
      松本佳彦
    • Organizer
      幾何セミナー(大阪大学)
    • Related Report
      2019 Annual Research Report
  • [Presentation] Canonical almost complex structures on ACH Einstein manifolds2019

    • Author(s)
      松本佳彦
    • Organizer
      微分トポロジーセミナー(京都大学)
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] CR structures, ACH-Einstein fillings, and almost complex structures2019

    • Author(s)
      松本佳彦
    • Organizer
      第25回複素幾何シンポジウム
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Canonical almost complex structures on ACH Einstein manifolds2019

    • Author(s)
      松本佳彦
    • Organizer
      幾何学セミナー(名古屋大学)
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Canonical almost complex structures on ACH Einstein manifolds2019

    • Author(s)
      松本佳彦
    • Organizer
      多変数関数論冬セミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Einstein asymptotically complex hyperbolic spaces and almost complex structures2019

    • Author(s)
      松本佳彦
    • Organizer
      2019 Taipei Conference on Geometric Invariance and Partial Differential Equations
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A construction of Poincae-Einstein metrics of cohomogeneity one on the ball2019

    • Author(s)
      松本佳彦
    • Organizer
      Geometry Luncheon Seminar (Pennsylvania State University)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Canonical almost complex structures on ACH Einstein manifolds2019

    • Author(s)
      松本佳彦
    • Organizer
      Geometry Seminar (Stanford University)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] CR geometry and ACH-Einstein metrics2018

    • Author(s)
      松本佳彦
    • Organizer
      QMAP Seminar (University of California, Davis)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A construction of Poincare-Einstein metrics of cohomogeneity one on the ball2018

    • Author(s)
      松本佳彦
    • Organizer
      Analytical Problems in Conformal Geometry and Applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Deformation of Einstein metrics and L2 cohomology on strictly pseudoconvex domains2018

    • Author(s)
      松本佳彦
    • Organizer
      Differential Geometry/PDE Seminar (University of Washington)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Deformation of Einstein metrics and L2 cohomology on strictly pseudoconvex domains2018

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      Geometry Seminar, Stanford University
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Deformation of Einstein metrics and L2 cohomology on strictly pseudoconvex domains2018

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      Differential Geometry Seminar, University of California, Riverside
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball2017

    • Author(s)
      松本佳彦
    • Organizer
      東京大学・複素解析幾何セミナー
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball2017

    • Author(s)
      松本佳彦
    • Organizer
      大阪大学・幾何セミナー
    • Related Report
      2017 Research-status Report
  • [Presentation] 有界強擬凸領域におけるCheng-Yau計量のEinstein変形とL2コホモロジー2017

    • Author(s)
      松本佳彦
    • Organizer
      京都大学・微分トポロジーセミナー
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Deformation of Einstein metrics and L2 cohomology on strictly pseudoconvex domains2017

    • Author(s)
      Yoshihiko Matsumoto
    • Organizer
      Special Session: Differential Geometry, The Third Pacific Rim Mathematical Association Congress
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Poincare-Einstein計量の基礎と展開2017

    • Author(s)
      松本佳彦
    • Organizer
      Geometric Analysis in Geometry and Topology 2017
    • Related Report
      2017 Research-status Report
  • [Remarks] 松本佳彦

    • URL

      http://www.math.sci.osaka-u.ac.jp/~matsumoto/

    • Related Report
      2019 Annual Research Report 2018 Research-status Report
  • [Remarks] 松本佳彦

    • URL

      http://www.math.sci.osaka-u.ac.jp/~matsumoto/index.php?lang=ja

    • Related Report
      2017 Research-status Report

URL: 

Published: 2017-04-28   Modified: 2022-02-22  

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