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Studies on 2-dimensional complex hyperbolic triangle groups

Research Project

Project/Area Number 22540212
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOkayama University of Science

Principal Investigator

KAMIYA Shigeyasu  岡山理科大学, 工学部, 教授 (80122381)

Co-Investigator(Kenkyū-buntansha) MURAKAMI Satoru  岡山理科大学, 理学部, 教授 (40123963)
YAMASAKI Masayuki  岡山理科大学, 理学部, 教授 (70174646)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords複素双曲三角群 / 複素双曲空間 / 離散群 / Jorgensenの不等式
Research Abstract

We discuss complex hyperbolic triangle groups of type (n,n,infinity;k) and obtain a new list of non-discrete groups. In particular, we show that if n >21, then complex hyperbolic triangle groups of type (n,n,infinity;k) are non-discrete. Also we find 10 discrete complex hyperbolic triangle groups of type (n,n,infinity;k).

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (30 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (10 results) (of which Peer Reviewed: 8 results) Presentation (20 results) (of which Invited: 3 results)

  • [Journal Article] Note on non-discrete complex hyperbolic triangle groups of type (n,n,∞;k)2013

    • Author(s)
      S.Kamiya
    • Journal Title

      Proc. Japan Academy

      Volume: SerA, 89 Issue: 8 Pages: 100-102

    • DOI

      10.3792/pjaa.89.100

    • NAID

      40019907086

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On controlled assembly maps2013

    • Author(s)
      M.Yamasaki
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B39 Pages: 197-214

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] J.R.Parker and J. Thompson : Non-discrete complex hyperbolic triangle groups of type (n,n,∞;k)2012

    • Author(s)
      S.Kamiya
    • Journal Title

      Canad, Math, Bull.

      Volume: 55(2) Issue: 2 Pages: 329-338

    • DOI

      10.4153/cmb-2011-094-8

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decomposition and variation-of-constants formula in the phrase space for integral equations2012

    • Author(s)
      H.Matsunaga, S.Murakami and Nguyen Van Minh
    • Journal Title

      Funkcial. Ekvac.

      Volume: 55, no.3 Pages: 479-520

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Formal adjoint equations and asymptotic formula for solutions of Volterra Difference equations with infinite delay2012

    • Author(s)
      H.Matsunaga, S.Murakami, Y.Nagabuchi and Y.Nakano
    • Journal Title

      J.Difference Equ. Appl.

      Volume: 18, no.1 Issue: 1 Pages: 57-88

    • DOI

      10.1080/10236198.2011.575070

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Complex hyperbolic triangle groups of type (n,n,∞;k)2011

    • Author(s)
      S.Kamiya
    • Journal Title

      Proc. of the 13th International conference on Real and Complex Analysis

      Volume: (Hiroshima Univ.) Pages: 52-57

    • NAID

      120007027897

    • Related Report
      2013 Final Research Report
  • [Journal Article] Complex hyperbolic triangle group of type (p,q,r;n)2011

    • Author(s)
      S.Kamiya
    • Journal Title

      Proceedings of the 13^<th> Conference on Real and Complex Analysis in Hiroshima (2010)

      Pages: 52-57

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Notes on complex hyperbolic triangle groups2010

    • Author(s)
      S.Kamiya, J.R.Parker and J. Thompson
    • Journal Title

      Conformal Geom. Dyn.

      Volume: 14 Pages: 202-218

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On stability and robust stability of positive linear Volterra equations in Banach Lattices2010

    • Author(s)
      S.Murakami and Pham Huu Anh Ngoc
    • Journal Title

      Central European Journal of Mathematics

      Volume: vol.8 Issue: 5 Pages: 966-984

    • DOI

      10.2478/s11533-010-0061-0

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Notes on complex hyperbolic triangle groups2010

    • Author(s)
      S.Kamiya, J.Parker, J.Thompson
    • Journal Title

      Conformal Geometry and Dynamics

      Volume: 14 Pages: 202-218

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Complex hyperbolic triangle groups2014

    • Author(s)
      S.Kamiya
    • Organizer
      「不動点とその周辺」研究集会
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2014-03-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups2013

    • Author(s)
      S.Kamiya
    • Organizer
      「リーマン面論の展望」研究集会
    • Place of Presentation
      山口大学
    • Year and Date
      2013-12-06
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic geometry2013

    • Author(s)
      S.Kamiya
    • Organizer
      ポテンシャルセミナー
    • Place of Presentation
      名城大学
    • Year and Date
      2013-11-29
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups of type (n, n, ∞;k)2012

    • Author(s)
      神谷茂保
    • Organizer
      松江複素解析セミナー
    • Place of Presentation
      島根大学
    • Year and Date
      2012-02-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] Complex hyperbolic triangle groups2011

    • Author(s)
      S.Kamiya
    • Organizer
      "Analysis and Geometry of Discrete Groups and Hyperbolic Spaces"研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-12-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups2011

    • Author(s)
      神谷茂保
    • Organizer
      Analysis and Geometry of Discrete Groups and Hyperbolic Spaces
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-12-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Complex hyperbolic triangle groups of type (n,n,∞,;k)2011

    • Author(s)
      S.Kamiya
    • Organizer
      Geometric and Topology Seminar
    • Place of Presentation
      National University of Singapore
    • Year and Date
      2011-03-02
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups2011

    • Author(s)
      神谷茂保
    • Organizer
      Geometry-Topology Seminar
    • Place of Presentation
      National University of Singapore
    • Year and Date
      2011-03-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Complex hyperbolic spaces II2011

    • Author(s)
      S.Kamiya
    • Place of Presentation
      Penang, Universiti Sains Malaysia
    • Year and Date
      2011-02-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups2011

    • Author(s)
      神谷茂保
    • Organizer
      Universiti Sains Malaysia
    • Place of Presentation
      Universiti Sains Malaysia
    • Year and Date
      2011-02-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Complex hyperbolic spaces I2011

    • Author(s)
      S.Kamiya
    • Place of Presentation
      Penang, Universiti Sains Malaysia
    • Year and Date
      2011-02-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic space2011

    • Author(s)
      神谷茂保
    • Organizer
      Universiti Sains Malaysia
    • Place of Presentation
      Universiti Sains Malaysia
    • Year and Date
      2011-02-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Complex hyperbolic triangle groups2011

    • Author(s)
      S.Kamiya
    • Organizer
      Conference on Complex Analysis and Discrete Groups
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-02-16
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups of type (n,n,∞;k)2011

    • Author(s)
      S.Kamiya
    • Organizer
      関数論セミナー
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-01-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups2011

    • Author(s)
      神谷茂保
    • Organizer
      複素解析セミナー
    • Place of Presentation
      大阪市立大学数学研究所
    • Year and Date
      2011-01-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Complex hyperbolic triangle groups2010

    • Author(s)
      S.Kamiya
    • Organizer
      The 13^<th > Conference on Real and Complex Analysis
    • Place of Presentation
      広島大学
    • Year and Date
      2010-12-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Complex hyperbolic triangle groups2010

    • Author(s)
      神谷茂保
    • Organizer
      The 13^<th> Conference on Real and Complex Analysis in Hiroshima (2010)
    • Place of Presentation
      広島大学
    • Year and Date
      2010-12-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Complex Hyperbolic Triangle Groups

    • Author(s)
      神谷茂保
    • Organizer
      ポテンシャル論セミナー
    • Place of Presentation
      名城大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Complex Hyperbolic Triangle Groups of type (n,n,infinity;k)

    • Author(s)
      神谷茂保
    • Organizer
      「リーマン面論の展望」研究集会
    • Place of Presentation
      山口大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Complex Hyperbolic Triangle Groups

    • Author(s)
      神谷茂保
    • Organizer
      「不動点とその周辺」研究集会
    • Place of Presentation
      奈良女子大学
    • Related Report
      2013 Annual Research Report
    • Invited

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Published: 2010-08-23   Modified: 2019-07-29  

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