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Moduli space of minimal surfaces with Galois Theory

Research Project

Project/Area Number 20740042
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionSaga University

Principal Investigator

SHODA Toshihiro  佐賀大学, 文化教育学部, 准教授 (10432957)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords極小曲面 / モジュライ空間 / ガロア理論 / モジュライ理論 / 平坦トーラス
Research Abstract

We usually call the set of all minimal surfaces" Moduli space of minimal surfaces". To consider the Moduli space of minimal surfaces, it is important to study Period map on the Moduli space of minimal surfaces. We have calculated periods of many examples of minimal surfaces. From the experiences, we conjecture that there may be symmetry by solvable group in Galois Theory. Thus, we will establish the Moduli theory of minimal surfaces in terms of the Galois Theory.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (28 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (3 results) (of which Peer Reviewed: 2 results) Presentation (19 results) Book (1 results) Remarks (5 results)

  • [Journal Article] An example of Jacobian variety and its applications to minimal surfaces2009

    • Author(s)
      T. Shoda
    • Journal Title

      Results in Mathematics

      Volume: 56 Pages: 23-39

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] An example of Jacobian variety and its applications to minimal surfaces2009

    • Author(s)
      T. Shoda
    • Journal Title

      Results in Mathematics 56

      Pages: 23-39

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] An example of Jacobian variety and its applications to minimal surfaces2009

    • Author(s)
      庄田敏宏
    • Journal Title

      Results in Mathematics 56

      Pages: 23-39

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] ユークリッド空間内の周期的極小曲面におけるMorse indexについて2012

    • Author(s)
      庄田敏宏
    • Organizer
      曲面論小研究集会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2012-03-19
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Morse indexによる極小曲面のモジュライ理論(江尻理論)について2012

    • Author(s)
      庄田敏宏
    • Organizer
      名城大学研究集会「極小曲面と幾何構造
    • Place of Presentation
      名城大学
    • Year and Date
      2012-03-06
    • Related Report
      2011 Final Research Report
  • [Presentation] Morse indexによる極小曲面のモジュライ理論(江尻理論)について2012

    • Author(s)
      庄田敏宏
    • Organizer
      名城大学研究集会「極小曲面と幾何構造」
    • Place of Presentation
      名城大学
    • Year and Date
      2012-03-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] 3次元平坦トーラス内の極小曲面のindexについて2011

    • Author(s)
      庄田敏宏
    • Organizer
      第58回幾何学シンポジウム・基調講演
    • Place of Presentation
      山口大学
    • Year and Date
      2011-08-27
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] On index and nullity of triply periodic minimal surfaces2011

    • Author(s)
      T. Shoda
    • Organizer
      Spanish-Japanese workshop on Differential Geometry
    • Place of Presentation
      Granada University
    • Year and Date
      2011-02-14
    • Related Report
      2011 Final Research Report
  • [Presentation] On index and nullity of triply periodic minimal surfaces Spanish Japanese Workshop on Differential Geometry2011

    • Author(s)
      T. Shoda
    • Place of Presentation
      Granada University
    • Year and Date
      2011-02-14
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On index and nullity of triply periodic minimal surfaces2011

    • Author(s)
      庄田敏宏
    • Organizer
      Spanish-Japanese Workshop on Differential Geometry
    • Place of Presentation
      グラナダ大学(スペイン)
    • Year and Date
      2011-02-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] 周期的極小曲面の諸性質について2010

    • Author(s)
      庄田敏宏
    • Organizer
      第57回幾何学シンポジウム
    • Place of Presentation
      神戸大学
    • Year and Date
      2010-08-07
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] R^3内の周期的極小曲面の縮約可能性について2009

    • Author(s)
      庄田敏宏
    • Organizer
      第121回日本数学会九州支部例会特別講演
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-10-17
    • Related Report
      2011 Final Research Report
  • [Presentation] R^3内の周期的極小曲面の縮約可能性について2009

    • Author(s)
      庄田敏宏
    • Organizer
      題121回日本数学会九州支部例会
    • Place of Presentation
      特別講演
    • Year and Date
      2009-10-17
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] R^3内の周期的極小曲面の縮約可能性について2009

    • Author(s)
      庄田敏宏
    • Organizer
      日本数学会九州支部例会
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-10-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 3次元平坦トーラス内の極小曲面について2009

    • Author(s)
      庄田敏宏
    • Organizer
      名城大学研究集会「幾何構造の諸相」
    • Place of Presentation
      名城大学
    • Year and Date
      2009-03-11
    • Related Report
      2011 Final Research Report
  • [Presentation] 3次元平坦トーラス内の極小曲面について2009

    • Author(s)
      庄田敏宏
    • Organizer
      名城大学幾何学研究集会「幾何構造の諸相」
    • Place of Presentation
      名城大学
    • Year and Date
      2009-03-11
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 3次元平坦トーラス内の極小曲面について2009

    • Author(s)
      庄田敏宏
    • Organizer
      幾何学研究集会「幾何構造の諸相」
    • Place of Presentation
      名城大学
    • Year and Date
      2009-03-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] On triply periodic minimal surfaces in R^32008

    • Author(s)
      T. Shoda
    • Organizer
      Integrable systems, Geometry and Visualization 2008
    • Place of Presentation
      Kyushu University
    • Year and Date
      2008-12-12
    • Related Report
      2011 Final Research Report
  • [Presentation] On triply periodic minimal surfaces in R^32008

    • Author(s)
      庄田敏宏
    • Organizer
      Integrable systems Geometry and Visualization 2008
    • Place of Presentation
      九州大学
    • Year and Date
      2008-12-12
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On triply periodic minimal surfaces in R^32008

    • Author(s)
      庄田敏宏
    • Organizer
      Integrable systems, Geometry and Visualiz ation 2008
    • Place of Presentation
      九州大学
    • Year and Date
      2008-12-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] Euclid空間内の極小曲面について2008

    • Author(s)
      庄田敏宏
    • Organizer
      第55回幾何学シンポジウム
    • Place of Presentation
      弘前大学
    • Year and Date
      2008-08-23
    • Related Report
      2011 Final Research Report
  • [Presentation] Euclid空間内の極小曲面について2008

    • Author(s)
      庄田敏宏
    • Organizer
      2008年度幾何学シンポジウム
    • Place of Presentation
      弘前大学
    • Year and Date
      2008-08-23
    • Related Report
      2010 Self-evaluation Report 2008 Annual Research Report
  • [Book] 集合・位相に親しむ2010

    • Author(s)
      庄田敏宏
    • Total Pages
      175
    • Publisher
      現代数学社
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Remarks]

    • URL

      http://extwww.cc.saga-u.ac.jp/~tshoda/shoda-home-j.html

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://extwww.cc.saga-u.ac.jp/~tshoda/shoda-home-j.html

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://extwww.cc.saga-u.ac.jp/~tshoda/shoda-home-j.html

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://extwww.cc.saga-u.ac.jp/~tshoda/shoda-home-j.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://extwww.cc.saga-u.ac.jp/~tshoda/shodahome-j.html

    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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