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Analysis of extremal Riemann surfaces and Klein surfaces

Research Project

Project/Area Number 25400147
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionAichi Institute of Technology

Principal Investigator

NAKAMURA Gou  愛知工業大学, 工学部, 教授 (50319208)

Co-Investigator(Renkei-kenkyūsha) NAKANISHI Toshihiro  島根大学, 総合理工学研究科, 教授 (00172354)
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords複素解析 / リーマン面 / クライン面 / 極値的円板 / 自己同型群 / モジュライ空間 / 解析学
Outline of Final Research Achievements

In the moduli space of closed Riemann surfaces of genus g, where g is greater than 1, we studied examples of those admitting a disk of the largest radius determined by genus (extremal disk). By considering characterization of their Fuchsian group representations and the structure of symmetricity, we obtained some results such as the groups of automorphisms and the locus of those surfaces in the Teichmuller space. We also made a similar analysis of non-orientable extremal Klein surfaces by considering their NEC group representations, and obtained some results.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (27 results)

All 2018 2017 2016 2015 2014 2013

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 5 results,  Acknowledgement Compliant: 4 results) Presentation (22 results) (of which Int'l Joint Research: 4 results,  Invited: 1 results)

  • [Journal Article] Generation of finite subgroups of the mapping class of genus 2 surface by Dehn twists2018

    • Author(s)
      Gou Nakamura and Toshihiro Nakanishi
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: 印刷中 Issue: 11 Pages: 3585-3594

    • DOI

      10.1016/j.jpaa.2018.01.002

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Compact non-orientable surfaces of genus 6 with extremal metric discs2016

    • Author(s)
      Gou Nakamura
    • Journal Title

      Conformal Geometry and Dynamics

      Volume: 20 Issue: 11 Pages: 218-234

    • DOI

      10.1090/ecgd/298

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Strong disk property for domains in open Riemann surfaces2016

    • Author(s)
      Makoto Abe, Gou Nakamura
    • Journal Title

      Filomat

      Volume: 30 Issue: 7 Pages: 1711-1716

    • DOI

      10.2298/fil1607711a

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Parametrization of Teichmuller space by trace functions and action of mapping class group2016

    • Author(s)
      Gou Nakamura and Toshihiro Nakanishi
    • Journal Title

      Conformal Geometry and Dynamics

      Volume: 20 Issue: 2 Pages: 25-42

    • DOI

      10.1090/ecgd/289

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Corrections to "Extremal disks and extremal surfaces of genus three"2014

    • Author(s)
      Gou Nakamura
    • Journal Title

      Kodai Mathematical Journal

      Volume: 37 Issue: 2 Pages: 475-480

    • DOI

      10.2996/kmj/1404393899

    • NAID

      130004949004

    • ISSN
      0386-5991, 1881-5472
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] 開Riemann面内の領域に対する強い円板的性質2017

    • Author(s)
      中村 豪、阿部 誠
    • Organizer
      ポテンシャル論セミナー、名城大学
    • Related Report
      2017 Annual Research Report
  • [Presentation] Strong disk property for domains in open Riemann surfaces2017

    • Author(s)
      中村 豪、阿部 誠
    • Organizer
      東工大複素解析セミナー、東京工業大学
    • Related Report
      2017 Annual Research Report
  • [Presentation] 熱方程式に関するDirichlet問題の多項式解2017

    • Author(s)
      鈴木 紀明、中村 豪
    • Organizer
      ポテンシャル論研究集会、大同大学
    • Related Report
      2017 Annual Research Report
  • [Presentation] 熱方程式に関するDirichlet問題の多項式解2017

    • Author(s)
      中村 豪、鈴木 紀明
    • Organizer
      日本数学会秋季総合分科会、山形大学
    • Related Report
      2017 Annual Research Report
  • [Presentation] 最大単射半径をもつ双曲曲面2017

    • Author(s)
      中村 豪
    • Organizer
      第60回函数論シンポジウム、セントコア山口
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Riemann surfaces and their maximal injectivity radii2017

    • Author(s)
      Nakamura Gou
    • Organizer
      Workshop "Prospects of Theory of Riemann surfaces", Yamaguchi University
    • Related Report
      2017 Annual Research Report
  • [Presentation] Presentation of finite subgroups of mapping class group of genus 2 surfaces by Dehn twists2017

    • Author(s)
      Nakamura Gou、Nakanishi Toshihiro
    • Organizer
      Summer school 2017 of the IMJ-PRG, Mapping class groups and their representations, Paris, France
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 開Riemann面内の領域に対する強い円板的性質2017

    • Author(s)
      阿部誠, 中村豪
    • Organizer
      2017年度日本数学会年会
    • Place of Presentation
      首都大学東京(東京都八王子市)
    • Related Report
      2016 Research-status Report
  • [Presentation] Compact non-orientable surfaces of genus 6 with extremal metric discs2016

    • Author(s)
      Gou Nakamura
    • Organizer
      Seminaire Geometrie
    • Place of Presentation
      Institut de Mathematiques de Bordeaux
    • Year and Date
      2016-01-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Compact non-orientable surfaces of genus 6 with extremal metric discs2016

    • Author(s)
      Gou Nakamura
    • Organizer
      Seminaire Teich
    • Place of Presentation
      Institut de Mathematiques de Marseille
    • Year and Date
      2016-01-08
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Compact Klein surfaces admitting automorphisms of maximum order2016

    • Author(s)
      Gou Nakamura
    • Organizer
      ポテンシャル論セミナー
    • Place of Presentation
      名城大学理工学部(愛知県名古屋市)
    • Related Report
      2016 Research-status Report
  • [Presentation] Hyperbolic surfaces with the largest maximal injectivity radius in the moduli space2016

    • Author(s)
      Gou Nakamura
    • Organizer
      東北複素解析セミナー
    • Place of Presentation
      東北大学情報科学研究科(宮城県仙台市)
    • Related Report
      2016 Research-status Report
  • [Presentation] The largest maximal injectivity radius of compact Riemann surfaces2016

    • Author(s)
      Gou Nakamura
    • Organizer
      リーマン面論の展望
    • Place of Presentation
      山口大学理学部(山口県山口市)
    • Related Report
      2016 Research-status Report
  • [Presentation] The largest maximal injectivity radius of hyperbolic surfaces2016

    • Author(s)
      Gou Nakamura
    • Organizer
      複素解析セミナー
    • Place of Presentation
      大阪市立大学数学研究所(大阪府大阪市)
    • Related Report
      2016 Research-status Report
  • [Presentation] Compact hyperbolic surfaces with extremal discs2015

    • Author(s)
      Gou Nakamura
    • Organizer
      Seminaire d’Analyse et Geometrie
    • Place of Presentation
      Institut de Mathematiques de Jussieu - Paris Rive Gauche
    • Year and Date
      2015-10-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] タイヒミュラー空間のトレース関数による座標系と写像類群2015

    • Author(s)
      中西敏浩、中村豪
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
  • [Presentation] Compact Riemann surfaces and dessins d'enfants2014

    • Author(s)
      Gou Nakamura
    • Organizer
      研究集会「リーマン面論の展望」
    • Place of Presentation
      山口大学(山口県山口市)
    • Year and Date
      2014-12-14
    • Related Report
      2014 Research-status Report
  • [Presentation] Klein surfaces and NEC groups derived from hyperbolic surfaces2014

    • Author(s)
      Gou Nakamura
    • Organizer
      The 7th MSJ-SI Hyperbolic Geometry and Geometric Group Theory
    • Place of Presentation
      東京大学(東京都目黒区)
    • Year and Date
      2014-07-31 – 2014-08-03
    • Related Report
      2014 Research-status Report
  • [Presentation] Compact Riemann surfaces and dessins d'enfants2013

    • Author(s)
      中村豪
    • Organizer
      ポテンシャル論セミナー
    • Place of Presentation
      名城大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Extremal disks and extremal surfaces2013

    • Author(s)
      中村豪
    • Organizer
      リーマン面の調和写像と擬等角写像
    • Place of Presentation
      山口大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Tori and symmetric Riemann surfaces of genus two2013

    • Author(s)
      中村豪
    • Organizer
      ポテンシャル論セミナー
    • Place of Presentation
      名城大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Symmetric extremal Riemann surfaces of genus two2013

    • Author(s)
      中村豪
    • Organizer
      リーマン面論の展望
    • Place of Presentation
      山口大学
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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