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Global construction of pleating coordinates of Teichmuller spaces and its applications

Research Project

Project/Area Number 19540194
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka City University

Principal Investigator

KOMORI Yohei  Osaka City University, 大学院・理学研究科, 准教授 (70264794)

Co-Investigator(Kenkyū-buntansha) 今吉 洋一  大阪市立大学, 大学院・理学研究科, 教授 (30091656)
佐官 謙一  大阪市立大学, 大学院・理学研究科, 准教授 (70110856)
作間 誠  広島大学, 大学院・理学研究科, 教授 (30178602)
須川 敏幸  広島大学, 大学院・理学研究科, 准教授 (30235858)
宮地 秀樹  東京電機大学, 理工学部, 准教授 (40385480)
Co-Investigator(Renkei-kenkyūsha) IMAYOSHI Yoichi  大阪市立大学, 大学院・理学研究科, 教授 (30091656)
SAKAN Kenichi  大阪市立大学, 大学院・理学研究科, 准教授 (70110856)
SAKUMA Makoto  広島大学, 大学院・理学研究科, 教授 (30178602)
SUGAWA Toshiyuki  東北大学, 大学院・情報科学研究科, 教授 (30235858)
MIYACHI Hideki  大阪大学, 大学院・理学研究科, 准教授 (40385480)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords複素解析 / リーマン面 / クライン群
Research Abstract

We estimate the Teichmuller distance between Riemann surfaces X and Y which is obtained from X byθ-grafting along a simple closed geodesic C. As anapplication we estimate the Teichmuller distance between the conformal boundary andthe convex core boundary of some regular b-groups of type (1,1) one of which gives acounterexample of K=2 conjecture. Also by means of geodesic length functions, werealize Teichmuller spaces of dimension 2 and 3 as convex polyhedron in real projective spaces.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (53 results)

All 2010 2009 2008 2007 Other

All Journal Article (25 results) (of which Peer Reviewed: 22 results) Presentation (27 results) Book (1 results)

  • [Journal Article] On holomorphic sections of a certain Kodaira surface revisited, Riemann Surfaces, Harmonic Maps and Visualization2009

    • Author(s)
      Yoichi Imayoshi, Yohei Komori, Toshihiro Nogi
    • Journal Title

      OCAMI Studies Volume 3

      Pages: 151-162

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Holomorphic sections of a holomorphic family of Riemann surfaces induced by a certain Kodaira surface2009

    • Author(s)
      Yoichi Imayoshi, Yohei Komori, Toshihiro Nogi
    • Journal Title

      Kodai Math.J. Vol.32, No.3

      Pages: 450-470

    • NAID

      130004687917

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On holomorphic sections of a certain Kodaira surface revisited2009

    • Author(s)
      Yoichi Imayoshi, Yohei Komori, Toshihiro Nogi
    • Journal Title

      Riemann Surfaces, Harmonic Maps and Visualization, OCAMI Studies Volume 3

      Pages: 151-162

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Holomorphic sections of a holomorphic family of Riemann surfaces induced by a certain Kodaira surface2009

    • Author(s)
      Yoichi Imayoshi, Yohei Komori, Toshihiro Nogi
    • Journal Title

      Kodai Mathemrical Journal Vol. 32, No. 3

      Pages: 450-470

    • NAID

      130004687917

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On holomorphic sections of a certain Kodaira surface revisited2009

    • Author(s)
      小森洋平
    • Journal Title

      OCAMI Studies 3

      Pages: 151-162

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Holomorphic sections of a holomorphic family of Riemann surfaces induced by a certain Kodaira surface2009

    • Author(s)
      小森洋平
    • Journal Title

      Kodai Mathematical Journal 32

      Pages: 450-470

    • NAID

      130004687917

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Drawing the complex projective structures on once-punctured tori2008

    • Author(s)
      Yohei Komori
    • Journal Title

      Geometry related to the theory of integrable systems RIMS 研究集会報告集 no.1605

      Pages: 81-89

    • Related Report
      2010 Final Research Report
  • [Journal Article] Modulus inequality for grafting and its application2008

    • Author(s)
      Yohei Komori
    • Journal Title

      Proceedings of the 15th ICFIDCAA

      Pages: 249-255

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Modulus inequality for grafting and its application2008

    • Author(s)
      Yohei Komori
    • Journal Title

      Complex Analysis and its Applications, OCAMI Studies Volume 2

      Pages: 249-254

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Drawing the complex projective structures On once-punctured tori2008

    • Author(s)
      Yohei Komori
    • Journal Title

      RIMS 研究集会報告集 1605巻

      Pages: 81-89

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] Modulus inequality for grafting and its application2008

    • Author(s)
      小森 洋平
    • Journal Title

      Proceedings of the 15^(th) ICFDICAA

      Pages: 249-255

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Drawing the complex proiective structures on once-punctured tori2008

    • Author(s)
      小森 洋平
    • Journal Title

      RIMS研究集会報告集 1605

      Pages: 81-89

    • Related Report
      2008 Annual Research Report
  • [Journal Article] On the shape of Bers-Maskit slices2007

    • Author(s)
      Yohei Komori, Jouni Parkkonen
    • Journal Title

      Ann.Acad.Sci.Fenn. 32

      Pages: 179-198

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy2007

    • Author(s)
      Yoichi Imayoshi
    • Journal Title

      Handbook of Teichmuller spaces Volume 2

      Pages: 93-130

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On bi-Lipschitz type inequalities for quasiconformal harmonic mappings2007

    • Author(s)
      Kenichi Sakan
    • Journal Title

      Ann.Acad.Sci.Fenn. 32

      Pages: 579-594

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Punctured torus groups and 2-bridge knot groups I2007

    • Author(s)
      Hirotaka Akiyoshi, Makoto Sakuma, Masaaki Wada, Yasushi Yamashita
    • Journal Title

      Lecture Notes in Mathematics, 1909, Springer

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Alexander transform of a spirallike function2007

    • Author(s)
      Toshiyuki Sugawa
    • Journal Title

      Journal Math.Anal.Appl. 325

      Pages: 608-611

    • NAID

      120000878103

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A reduction for asymptotic Teichmuller spaces2007

    • Author(s)
      Hideki Miyachi
    • Journal Title

      Ann.Acad.Sci.Fenn. 32

      Pages: 55-71

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the shape of Bers-Maskit slices2007

    • Author(s)
      Yohei Komori, Jouni Parkonen
    • Journal Title

      Ann.Acad.Sci.Fenn. 32

      Pages: 179-198

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the shape of Bers-Maskit slices2007

    • Author(s)
      小森 洋平
    • Journal Title

      Ann. Acad. Sci. Fenn. 32

      Pages: 179-198

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On bi-Lipschitz type inequalities for quasiconformal harmonic mappings2007

    • Author(s)
      佐官 謙一
    • Journal Title

      Ann. Acad. Sci. Fenn 32

      Pages: 579-594

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Alexander transform of a spirallike function2007

    • Author(s)
      須川 敏幸
    • Journal Title

      Journal Math. Anal. Appl. 325

      Pages: 608-611

    • NAID

      120000878103

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A reduction for asymptotic Teichmuller spaces2007

    • Author(s)
      宮地 秀樹
    • Journal Title

      Ann. Acad. Sci. Fenn 32

      Pages: 55-71

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy

    • Author(s)
      今吉 洋一
    • Journal Title

      Handbook of Teichmuller spaces、Volume 2. (掲載確定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Epimorphisms between 2-bridge knot groups

    • Author(s)
      作間 誠
    • Journal Title

      Geometry and Topology Monograph (掲載確定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Polyhedral realization of a Thurston compactification2010

    • Author(s)
      小森洋平
    • Organizer
      Oberwolfach Workshop "Teichmuller Theory"
    • Place of Presentation
      Oberwolfach研究所(ドイツ)
    • Year and Date
      2010-12-03
    • Related Report
      2010 Final Research Report
  • [Presentation] Polyhedral realization of a Thurston compactification2010

    • Author(s)
      小森洋平
    • Organizer
      Oberwolfach Workshop "Teichmuller Theory"
    • Place of Presentation
      Oberwolfach研究所(ドイツ)(招待講演)
    • Year and Date
      2010-12-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] The Banach-Tarski paradox for symmetric spaces2010

    • Author(s)
      小森洋平
    • Organizer
      Colloquium
    • Place of Presentation
      Fribourg大学(スイス)(招待講演)
    • Year and Date
      2010-11-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Cook hat and crown2010

    • Author(s)
      小森洋平
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Cook-hats and crowns2010

    • Author(s)
      小森洋平
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] ある種数2のリーマン面の正則切断について2010

    • Author(s)
      小森洋平
    • Organizer
      日本数学会春期総合分科会
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2010-03-24
    • Related Report
      2010 Final Research Report
  • [Presentation] ある種数2のリーマン面の正則切断について2010

    • Author(s)
      小森洋平
    • Organizer
      日本数学会
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2010-03-24
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] ある種数2のリーマン面の正則族の正則切断について2010

    • Author(s)
      小森洋平
    • Organizer
      日本数学会
    • Place of Presentation
      慶応義塾大学理工学部
    • Year and Date
      2010-03-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] 種数1のリーマン面上の退化族の構成について2009

    • Author(s)
      小森洋平
    • Organizer
      低次元トポロジーセミナー
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2009-12-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Holomorphic sections of a holomorphic family of Riemann surfacesinduced by a certain Kodaira surface2009

    • Author(s)
      小森洋平
    • Organizer
      ネバリンナ・コロ キウム
    • Place of Presentation
      京都大学
    • Year and Date
      2009-09-08
    • Related Report
      2010 Final Research Report
  • [Presentation] Holomorphic sections of a holomorphic family of Riemann surfacesinduced by a certain Kodaira surface2009

    • Author(s)
      小森洋平
    • Organizer
      ネバリンナ・コロキウム
    • Place of Presentation
      京都大学
    • Year and Date
      2009-09-08
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 平坦構造からのタイヒミユラー空間入門2008

    • Author(s)
      小森 洋平
    • Organizer
      函数論サマーセミナー
    • Place of Presentation
      マホロバマインズ 三浦
    • Year and Date
      2008-08-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] タイヒミュラー空間の複素解析的側面2008

    • Author(s)
      小森洋平
    • Organizer
      力学系集会
    • Place of Presentation
      九州大学
    • Year and Date
      2008-05-19
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] タイヒミユラー空間論の複素解析的側面2008

    • Author(s)
      小森 洋平
    • Organizer
      Flat Surfaces and the Teichm"uller Geodesic Flow
    • Place of Presentation
      九州大学理学部
    • Year and Date
      2008-05-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] On asymptotically sharp inequalities for quasiconformalharmonic mappings2008

    • Author(s)
      佐官 謙一
    • Organizer
      日本数学会関数論分科会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2008-03-29
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the holomorphic sections of a holomorphic families of Riemann surf aces induced by a Kodaira surface2007

    • Author(s)
      今吉 洋一
    • Organizer
      Workshop on infinite dimensional Teichmuller spaces
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-11-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the Gardiner-Masur boundary of Teichmuller space2007

    • Author(s)
      宮地 秀樹
    • Organizer
      Workshop on infinite dimensional Teichmuller spaces
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-11-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] On counterexamples to the equivariant K=2 conjecture2007

    • Author(s)
      小森洋平
    • Organizer
      日本数学会関数論分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] On counterexample to the equivariant K=2 conjecture2007

    • Author(s)
      小森洋平
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] On counterexample to the equivariant K=2 conjecture2007

    • Author(s)
      小森 洋平
    • Organizer
      日本数学会関数論分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Hypergeometric functions and hyperbolic metric2007

    • Author(s)
      須川 敏幸
    • Organizer
      日本数学会関数論分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Drawing the complex projective structures on once-punctured tori2007

    • Author(s)
      小森洋平
    • Organizer
      研究集会「可積分系に関わる幾何学」
    • Place of Presentation
      京大数理研
    • Year and Date
      2007-09-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Margulis tubes and bending loci of punctured torus groups2007

    • Author(s)
      小森洋平
    • Organizer
      Workshop Hyperbolic Volume
    • Place of Presentation
      フリブール大学(スイス)
    • Year and Date
      2007-07-03
    • Related Report
      2010 Final Research Report
  • [Presentation] Margulis tubes and bending loci of punctured torus groups2007

    • Author(s)
      Yohei Komori
    • Organizer
      Workshop Hyperbolic Volume
    • Place of Presentation
      フリブール大学 (スイス)
    • Year and Date
      2007-07-03
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] On the distance between two Seifert surfaces of a knot2007

    • Author(s)
      作間 誠
    • Organizer
      Geometric Topology Conference
    • Place of Presentation
      北京大学
    • Year and Date
      2007-06-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] Drawing the complex projective structures on once-punctured tori

    • Author(s)
      小森洋平
    • Organizer
      微分幾何セミナー
    • Place of Presentation
      マックスプラ ンク研究所(ドイツ)
    • Related Report
      2010 Final Research Report
  • [Presentation] Drawing the complex projective structures on once-punctured tori

    • Author(s)
      小森洋平
    • Organizer
      幾何セミナー
    • Place of Presentation
      モンペリエ大学(フランス)
    • Related Report
      2010 Final Research Report
  • [Book] Punctured torus groups and 2-bridge knot groups (I)2007

    • Author(s)
      作間 誠
    • Total Pages
      295
    • Publisher
      Springer Verlag
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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