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Global properties of surfaces which possess the Wewierstrass type representation formulae and their singularities

Research Project

Project/Area Number 25800047
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionOkayama University

Principal Investigator

Fujimori Shoichi  岡山大学, 自然科学研究科, 准教授 (00452706)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsワイエルストラス型表現公式 / 極小曲面 / 極大曲面 / 平均曲率0曲面 / 特異点 / 解析的延長 / 退化極限 / クリストッフェル変換 / 光的直線
Outline of Final Research Achievements

The global properties of surfaces which possess Weierstrass type representation formulae and their singularities were investigated. For periodic minimal surfaces in Euclidean 3-space, the moduli space and its degenerate limits were studied. For zero mean curvature surfaces with mixed causal type in Minkowski 3-space, many families of such surfaces were constructed, and the embeddedness of some of them were proved. Moreover, relation between zero mean curvature surfaces and 2-dimensional fluid mechanics was observed.

Report

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

    (22 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (3 results) Journal Article (11 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 11 results,  Acknowledgement Compliant: 6 results,  Open Access: 4 results) Presentation (5 results) (of which Invited: 3 results) Remarks (3 results)

  • [Int'l Joint Research] ウィーン工科大学(オーストリア)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] 高麗大学校(韓国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] アシュート大学(エジプト)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space2017

    • Author(s)
      Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, and Kotaro Yamada
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 印刷中

    • NAID

      120006312701

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Entite zero-mean curvature graphs of mixed type in Lorents-Minkowski 3-space2016

    • Author(s)
      S. Fujimori, Y. Kawakami, M. Kokubu, W. Rossman, M. Umehara, K. Yamada
    • Journal Title

      Quart. J. Math.

      Volume: 67 Pages: 1-37

    • DOI

      10.1093/qmath/haw038

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Maximal surfaces in Minkowski 3-space with non-trivial topology and corresponding CMC 1 surfaces in de Sitter 3-space2016

    • Author(s)
      Shoichi Fujimori, Samah Gaber Mohamed, and Mason Pember
    • Journal Title

      Kobe Journal of Mathematics

      Volume: 33 Pages: 1-12

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Minimal surfaces with two ends which have the least total absolute curvature2016

    • Author(s)
      Shoichi Fujimori and Toshihiro Shoda
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 282 Issue: 1 Pages: 107-144

    • DOI

      10.2140/pjm.2016.282.107

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Computer Graphics in Minimal Surface Theory2015

    • Author(s)
      Shoichi Fujimori
    • Journal Title

      Mathematical Progress in Expressive Image Synthesis II, Mathematics for Industry

      Volume: 18 Pages: 9-18

    • DOI

      10.1007/978-4-431-55483-7_2

    • ISBN
      9784431554820, 9784431554837
    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Schwarz maps for the hypergeometric differential equation2015

    • Author(s)
      Fujimori, Shoichi; Noro, Masayuki; Saji, Kentaro; Sasaki, Takeshi; Yoshida, Masaaki.
    • Journal Title

      Internat. J. Math.

      Volume: 26 Issue: 06 Pages: 1541002-1541002

    • DOI

      10.1142/s0129167x15410025

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] A remark on limits of triply periodic minimal surfaces of genus 32015

    • Author(s)
      N. Ejiri, S. Fujimori and T. Shoda
    • Journal Title

      Topology and its Applications

      Volume: 196 Pages: 880-903

    • DOI

      10.1016/j.topol.2015.05.014

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Zero mean curvature surfaces in Lorentz-Minkowski 3-space and 2-dimensional fluid mechanics2015

    • Author(s)
      Shoichi Fujimori, Young Wook Kim, Sung-Eun Koh, Wayne Rossman, Heayong Shin, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    • Journal Title

      Mathematical Journal of Okayama University

      Volume: 57 Pages: 173-200

    • NAID

      120005525349

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line2015

    • Author(s)
      Shoichi Fujimori, Young Wook Kim, Sung-Eun Koh, Wayne Rossman, Heayong Shin, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 52 Pages: 285-297

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Computer graphics and minimal surfaces2014

    • Author(s)
      Shoichi Fujimori
    • Journal Title

      MI Lecture Notes

      Volume: 58 Pages: 36-42

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space2014

    • Author(s)
      S. Fujimori, W. Rossman, M. Umehara, K. Yamada and S.-D. Yang
    • Journal Title

      Michigan Math. J.

      Volume: 63 Issue: 1 Pages: 189-207

    • DOI

      10.1307/mmj/1395234364

    • Related Report
      2013 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 3次元Lorentz-Minkowski空間の平均曲率0曲面2016

    • Author(s)
      藤森祥一
    • Organizer
      RIMS研究集会「部分多様体の微分幾何学的研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 2つのエンドを持つ極小曲面の全曲率2016

    • Author(s)
      藤森祥一
    • Organizer
      第63回幾何学シンポジウム
    • Place of Presentation
      岡山大学
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Jorge-Meeks型極大曲面の解析的拡張,2015

    • Author(s)
      藤森祥一
    • 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
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] 3重周期的極小曲面の退化極限2014

    • Author(s)
      藤森祥一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
  • [Presentation] 3次元Lorentz-Minkowski空間内の平均曲率0埋め込み2013

    • Author(s)
      藤森祥一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks] 藤森祥一のウェブページ

    • URL

      http://www.math.okayama-u.ac.jp/~fujimori/index-j.html

    • Related Report
      2016 Annual Research Report
  • [Remarks] 藤森祥一のホームページ

    • URL

      http://www.math.okayama-u.ac.jp/~fujimori/index-j.html

    • Related Report
      2015 Research-status Report 2014 Research-status Report
  • [Remarks] 藤森祥一のホームページ

    • URL

      http://www.math.okayama-u.ac.jp/~fujimori/index-j.html

    • Related Report
      2013 Research-status Report

URL: 

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

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