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Geometric analysis on metrics of the moduli of punctured Riemann surfaces

Research Project

Project/Area Number 18K03338
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionKagoshima University

Principal Investigator

Obitsu Kunio  鹿児島大学, 理工学域理学系, 准教授 (00325763)

Co-Investigator(Kenkyū-buntansha) 愛甲 正  鹿児島大学, 理工学域理学系, 教授 (00192831)
近藤 剛史  鹿児島大学, 理工学域理学系, 准教授 (60467446)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsリーマン面 / タイヒミュラー空間 / ケイラー計量 / 漸近挙動 / アイゼンシュタイン級数 / 双曲計量 / Eisenstein級数 / ケーラー計量 / 漸近展開 / モジュライ空間 / 尖点つきリーマン面 / モジュライ / 漸近解析
Outline of Final Research Achievements

Main goal of this project was that we would reveal fundamental properties of the Takhtajan-Zograf metric on Teichmuller spaces of punctured Riemann surfaces. one of the main results obtained in this project is the improvement of the estimates of asymptotic boundary behaviors of the Takhtajan-Zograf metric near the boundary of Teichmuller spaces. In the results of my previous collaborate research, there remained unsatisfactory estimates of the main terms of the astmptotics of the metric. Then, in the project, we tried to improve the upper bound of degree of the main term and succeeded to get the optimal order estimate. On the other hand, we failed to improve the lower bound of degree of the main term, which remains to improve.

Academic Significance and Societal Importance of the Research Achievements

Takhtajan-Zograf計量は、Weil-Petersson計量のタイヒミュラー空間の境界における漸近展開の第2項として現れることを、2008年にWolpert氏と共同で示したが。この結果はここ数年、何人かの数理物理学者によって注目され、これを応用した超弦理論の研究が進み始めている。これは期待した通りの研究の進展であり、今後ともTakhtajan-Zograf計量の基本的性質を探求していくことは、大いに意義あることと考えられる。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (10 results)

All 2021 2020 2019 2018

All Presentation (8 results) (of which Int'l Joint Research: 1 results,  Invited: 7 results) Funded Workshop (2 results)

  • [Presentation] Takhtajan-Zograf計量の最近の進展について2021

    • Author(s)
      小櫃邦夫
    • Organizer
      東京工業大学複素解析セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] グラフのラプラシアンと全域森の数え上げ2020

    • Author(s)
      近藤剛史
    • Organizer
      「測地線及び関連する諸問題」
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 擬等角変分の方法について2019

    • Author(s)
      小櫃邦夫
    • Organizer
      Beltrami方程式勉強会 II
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Coxeter 群に対する Wirtinger の不等式の変種2019

    • Author(s)
      近藤剛史
    • Organizer
      測地線および関連する諸問題
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Coxeter 群に対する Wirtinger の不等式の変種2019

    • Author(s)
      近藤剛史
    • Organizer
      幾何学と組合せ論2019
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Negative vector bundles and complex Finsler geometry2018

    • Author(s)
      愛甲正
    • Organizer
      23rd International Summer School on Global Analysis and Applications, Brasov, Romania
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] One-sided projective changes of Finsler connections2018

    • Author(s)
      愛甲正
    • Organizer
      第53回フィンスラー幾何学シンポジウム、福岡工業大学
    • Related Report
      2018 Research-status Report
  • [Presentation] Coxeter 群に対する Wirtinger の不等式の変種2018

    • Author(s)
      近藤剛史
    • Organizer
      福岡大学微分幾何研究集会2018(招待講演)
    • Related Report
      2018 Research-status Report
    • Invited
  • [Funded Workshop] The Mathematical Legacy of Maryam Mirzakhani2018

    • Related Report
      2018 Research-status Report
  • [Funded Workshop] Workshop on Geometry of Teichmuller Space2018

    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2024-01-30  

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