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Studies on compactifications of Teichmuller spaces

Research Project

Project/Area Number 23540221
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionWaseda University (2012-2013)
Osaka City University (2011)

Principal Investigator

KOMORI Yohei  早稲田大学, 教育・総合科学学術院, 教授 (70264794)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords複素解析 / リーマン面 / 複素解析幾何 / 幾何学的群論 / 国際研究者交流
Research Abstract

Except Riemann surfaces conformal to Riemann spheres minus disks and one or two points, I showed that Teichmuller spaces of RIemann surfaces of topologically finite types can be realized as polyhedron in finite dimensional real projective spaces by means of length functions of suitable choices of simple closed geodesics. Thurston boundaries of Teichmuller spaces were also considered. I also constructed degenerate families of Riemann surfaces over tori explicitly, and determined their singular fibers and holomorphic sections.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (32 results)

All 2014 2013 2012 Other

All Journal Article (9 results) (of which Peer Reviewed: 8 results) Presentation (23 results) (of which Invited: 5 results)

  • [Journal Article] Polyhedral Realization of Thurston Compactification2014

    • Author(s)
      M. Gendulphe and Y. Komori
    • Journal Title

      The Annales de la Faculte des Sciences de Toulouse, Ser.6

      Volume: Ser.6, Vol.23 Pages: 95-114

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Polyhedral Realization of a Thurston Compactification2014

    • Author(s)
      Matthieu Gendulphe and Yohei Komori
    • Journal Title

      The Annales de la Faculté des Sciences de Toulouse

      Volume: Ser.6, Vol.23 Pages: 95-114

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the growth of hyperbolic 3-dimensional generalized simplex reflection groups2012

    • Author(s)
      Y. Komori and Y. Umemoto
    • Journal Title

      Proc. Japan Acad

      Volume: 88, Ser. A Pages: 62-65

    • NAID

      40019228034

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cook-hats and crowns, Quasiconformal mappings, Riemann surfaces, and Teichmuller spaces2012

    • Author(s)
      Y. Komori
    • Journal Title

      Contemp. Math

      Volume: 575, Amer. Math. Soc Pages: 253-262

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Linear slices of the quasi-Fuchsian space of punctured tori2012

    • Author(s)
      Y. Komori and Y. Yamashita
    • Journal Title

      Conform. Geom. Dyn

      Volume: 16 Pages: 89-102

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Projective embeddings of the Teichmuller spaces of bordered Riemann surfaces2012

    • Author(s)
      Y. Komori
    • Journal Title

      数理解析研究所講究録

      Volume: 1777 Pages: 75-83

    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Journal Article] Cook-hats and crowns2012

    • Author(s)
      Yohei Komori
    • Journal Title

      Contemporary Mathematics

      Volume: 575 Pages: 253-262

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the growth of hyperbolic 3-dimensional generalized simplex reflection groups2012

    • Author(s)
      Yohei Komori and Yuriko Umemoto
    • Journal Title

      Proc. Japan Acad., Ser A

      Volume: 88 Pages: 62-65

    • NAID

      40019228034

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Linear Slices of the Quasifuchsian Space of Punctured Tori2012

    • Author(s)
      Yohei Komori and Yasushi Yamashita
    • Journal Title

      Conformal Geometry and Dynamics, AMS

      Volume: 16 Pages: 89-102

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] On degenerate families of Riemann surfaces over elliptic curves2014

    • Author(s)
      Y. Komori
    • Organizer
      離散群と双曲空間の複素解析とトポロジー
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-01-20
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] On degenerate families of Riemann surfaces over elliptic curves2014

    • Author(s)
      Y. Komori
    • Organizer
      Rigidity School
    • Place of Presentation
      Tokyo, 東京大学
    • Year and Date
      2014-01-07
    • Related Report
      2013 Final Research Report
  • [Presentation] On degenerate families of Riemann surfaces over elliptic curves2014

    • Author(s)
      Yohei Komori
    • Organizer
      Rigidity School, Tokyo
    • Place of Presentation
      東京大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] トーラス上のリーマン面の退化族について2013

    • Author(s)
      小森洋平
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-26
    • Related Report
      2013 Final Research Report
  • [Presentation] トーラス上のリーマン面の退化族について2013

    • Author(s)
      小森洋平
    • Organizer
      リーマン面に関連する位相幾何学
    • Place of Presentation
      東京大学
    • Year and Date
      2013-08-27
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] トーラス上の種数2のリーマン面の退化族について2013

    • Author(s)
      小森洋平
    • Organizer
      日本数学会春期総合分科会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Arithmetic aspects of growth rates of hyperbolic Coxeter groups2013

    • Author(s)
      Y. Komori
    • Organizer
      国際 研究集会「 Growth and Mahler measures in geometry and topology 」
    • Place of Presentation
      ミッタ ク・レフラー研究所, スウェーデン
    • Related Report
      2013 Final Research Report
  • [Presentation] On a degenerate family of Riemann surfaces of genus two over an elliptic curve2013

    • Author(s)
      Y. Komori
    • Organizer
      国際研究集会「 Branched Coverings, Degenerations, and Related Topics 」
    • Place of Presentation
      首都大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Arithmetic aspects of growth rates of hyperbolic Coxeter groups2013

    • Author(s)
      Yohei Komori
    • Organizer
      Growth and Mahler measures in geometry and topology
    • Place of Presentation
      Mittag-Leffler 研究所、スウェーデン
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] トーラス上のリーマン面の退化族について2013

    • Author(s)
      小森洋平
    • Organizer
      日本数学会秋期総合分科会函数論分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] On a degenerate family of Riemann surfaces induced by a certain Kodaira surface2012

    • Author(s)
      Y. Komori
    • Organizer
      Topology seminar
    • Place of Presentation
      ストラスブール大学, フランス
    • Year and Date
      2012-09-13
    • Related Report
      2013 Final Research Report
  • [Presentation] On the growth rates of 3-dimensional generalized simplex reflection groups2012

    • Author(s)
      小森洋平
    • Organizer
      日本数学会春期総合分科会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Linear slices of the quasifuchsian space of punctured tori2012

    • Author(s)
      Y. Komori
    • Organizer
      国際研究集会「 Progress in Low-dimensional Topology: Teichmuller t heory and 3-manifold groups 」
    • Place of Presentation
      オーフス大学, デンマーク
    • Related Report
      2013 Final Research Report
  • [Presentation] トーラス上の種数 2 のリーマン面の退化族について

    • Author(s)
      小森洋平
    • Organizer
      日本数学会春期総合分科会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] On a degenerate family of Riemann surfaces of genus two over an elliptic curve

    • Author(s)
      Yohei Komori
    • Organizer
      研究集会 Branched Coverings, Degenerations, and Related Topics
    • Place of Presentation
      首都大学東京
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On growth rates of 3-dimensional hyperbolic Coxeter prisms

    • Author(s)
      小森洋平
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] On a degenerate family of Riemann surfaces induced by a certain Kodaira surface

    • Author(s)
      Yohei Komori
    • Organizer
      トポロジーセミナー
    • Place of Presentation
      ストラスブール大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Linear slices of the quasifuchsian space of punctured tori

    • Author(s)
      Yohei Komori
    • Organizer
      国際研究集会Progress in low-dimensional topology: Teichmuller theory and 3-manifold groups
    • Place of Presentation
      オーフス大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On the growth rates of 3-dimensional generalized simplex reflection groups

    • Author(s)
      小森洋平、梅本 悠莉子
    • Organizer
      日本数学会春期総合分科会
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Cone lemma とその応用

    • Author(s)
      小森洋平
    • Organizer
      ワークショップ「クライン群とコンピュータ・グラフィックス」(招待講演)
    • Place of Presentation
      名古屋大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Linear slices of the quasifuchsian space of punctured tori

    • Author(s)
      小森洋平
    • Organizer
      第19回有限無限次元複素解析国際会議(招待講演)
    • Place of Presentation
      アステールプラザ広島
    • Related Report
      2011 Research-status Report
  • [Presentation] On Dirichlet polyhedra for generalized simplex groups

    • Author(s)
      小森洋平、梅本 悠莉子
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      信州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Cook-Hats and Crowns

    • Author(s)
      小森洋平
    • Organizer
      数理解析研究所短期共同研究「群の表現及び表現空間の幾何学的・解析的研究」(招待講演)
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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