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Singularities and balancing conditions on the theory of minimal surfaces and related geometric variational problems

Research Project

Project/Area Number 22540232
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KATO Shin  大阪市立大学, 大学院理学研究科, 准教授 (10243354)

Co-Investigator(Kenkyū-buntansha) TAKAHASHI Futoshi  大阪市立大学, 大学院理学研究科, 教授 (10374901)
KOMORI Yohei  早稲田大学, 教育学部, 教授 (70264794)
Co-Investigator(Renkei-kenkyūsha) KASUE Atsushi  金沢大学, 理工学研究域数物科学系, 教授 (40152657)
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords多様体上の解析 / 極小曲面
Outline of Final Research Achievements

We formulated the condition for the existence of n-noids of genus 1 in the Euclidian 3-space whose complete system of representatives of poles of Gauss map and that of ends coincide with each other. Moreover, we constructed new examples of such n-noids. We also decided the indices and nullities of n-noids of genes 0 under the condition that n is 4, or n is greater than 4 and the n-noid is symmetric in a sense. Moreover, we got a result on the relation between flux and nullity of n-noids. We also constructed a 1-parameter family of n-noids defined on punctured projective planes under the condition that n is an even number greater than or equal to 4, and that all of the ends of the surface is catenoidal type. It should be remarked here that only known examples of n-noids defined on punctured projective planes have odd number of planer ends.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (5 results)

All 2015 2014 2012

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (3 results) (of which Invited: 2 results)

  • [Journal Article] Minimal surfaces of genus one with catenoidal ends II2015

    • Author(s)
      S. Kato and H. Muroya
    • Journal Title

      Osaka J. Math.

      Volume: 52 Pages: 307-371

    • NAID

      120005986358

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimal surfaces of genus one with catenoidal ends2012

    • Author(s)
      Shin KATO
    • Journal Title

      Osaka J. Math.

      Volume: 49 Pages: 931-992

    • NAID

      120005174155

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] n-noid の index, nullity と flux2015

    • Author(s)
      加藤 信
    • Organizer
      2015名城大学幾何学研究集会「幾何構造の融合と発展」
    • Place of Presentation
      名城大学理工学部(愛知県名古屋市)
    • Year and Date
      2015-03-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 向き付け不可能な n-end catenoid は存在するか?2015

    • Author(s)
      加藤 信
    • Organizer
      淡路島幾何学研究集会2015
    • Place of Presentation
      国民宿舎慶野松原荘(兵庫県南あわじ市)
    • Year and Date
      2015-01-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] Index, nullity and flux of n-noids2014

    • Author(s)
      加藤 信
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村南阿蘇(熊本県高森町)
    • Year and Date
      2014-09-20
    • Related Report
      2014 Annual Research Report
    • Invited

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

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