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Research on stability and global properties of solutions of geometric variational problems

Research Project

Project/Area Number 19540217
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionNara Women's University

Principal Investigator

KOISO Miyuki  Nara Women's University, 理学部, 教授 (10178189)

Co-Investigator(Kenkyū-buntansha) FUJIOKA Atsushi  一橋大学, 大学院・経済学研究科, 准教授 (30293335)
ANDO Naoya  熊本大学, 大学院・自然科学研究科, 准教授 (50359965)
Research Collaborator PALMER Bennett  米国・アイダホ州立大学, 教授
PICCIONE Paolo  ブラジル・サンパウロ大学, 教授
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords変分法 / 変分問題 / capillary surface / Delaunay曲面 / 非等方的表面エネルギー / 非等方的平均曲率一定曲面 / 平均曲率一定曲面 / Wulff図形 / ウルフ図形 / 国際研究者交流 / アメリカ合衆国 : ブラジル / unduloid / アメリカ合衆国
Research Abstract

We studied equilibrium surfaces for anisotropic surface energy with volume constraint (CAMC surfaces). We obtained many important results about geometry and stability for CAMC surfaces with free boundary on two parallel planes. Moreover, we proved a uniqueness theorem for closed CAMC surfaces.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (36 results)

All 2010 2009 2008 2007 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (22 results) Remarks (4 results)

  • [Journal Article] Anisotropic umbilic points and Hopf's theorem for surfaces with constant anisotropic mean curvature2010

    • Author(s)
      Miyuki Koiso, Bennett Palmer
    • Journal Title

      Indiana University Mathematics Journal Vol.59,No.1

      Pages: 79-90

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Riemann Surfaces, Harmonic Maps and Visualization2010

    • Author(s)
      Miyuki Koiso, Bennett Palmer
    • Journal Title

      OCAMI Studies Volume3

      Pages: 129-144

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Anisotropic Surface Energy2010

    • Author(s)
      Miyuki Koiso
    • Journal Title

      OCAMI Studies Vol.3

      Pages: 129-144

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Anisotropic umbilic points and Hopfs Theorem for surfaces with constant anisotropic mean curvature2010

    • Author(s)
      Miyuki Koiso
    • Journal Title

      Indiana University Mathematics Journal Vol.59(未定(掲載決定))

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equilibria for anisotropic surface energies and the Gielis formula2008

    • Author(s)
      Miyuki Koiso, Bennett Palmer
    • Journal Title

      Forma Vol.23,No.1

      Pages: 1-8

    • NAID

      10026051060

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rolling construction for anisotropic Delaunay surfaces2008

    • Author(s)
      Miyuki Koiso, Bennett Palmer
    • Journal Title

      Pacific Journal of Mathematics Vol.234,No.2

      Pages: 345-378

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Equilibria for anisotropio surface energies and the Gielis formula2008

    • Author(s)
      Miyuki Koiso
    • Journal Title

      Forma 23

      Pages: 1-8

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness theorems for stable anisotropic capillary surfaces2007

    • Author(s)
      Miyuki Koiso, Bennett Palmer
    • Journal Title

      SIAM Journal on Mathematical Analysis Vol.39,No.3

      Pages: 721-741

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Anisotropic capillary surfaces with wetting energy2007

    • Author(s)
      Miyuki Koiso, Bennett Palmer
    • Journal Title

      Calculus of Variations and Partial Differential Equations Vol.29,No.3

      Pages: 295-345

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Equilibria for anisotropic surface energies and the Gielis formula

    • Author(s)
      Miyuki Koiso
    • Journal Title

      FORMA (未定)(掲載決定)

    • NAID

      10026051060

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Stability and bifurcation for solutions of isoperimetric type problems2010

    • Author(s)
      Miyuki Koiso
    • Organizer
      The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis
    • Place of Presentation
      Department of Mathematics, National Taiwan University, Taiwan
    • Year and Date
      2010-03-22
    • Related Report
      2009 Final Research Report
  • [Presentation] Stability and bifurcation for solutions of isoperimetric type problems2010

    • Author(s)
      Miyuki Koiso
    • Organizer
      The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis
    • Place of Presentation
      National Taiwan University, Taiwan
    • Year and Date
      2010-03-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] Geometric variational problems and bifurcation theory2010

    • Author(s)
      Miyuki Koiso
    • Organizer
      The First CREST-SBM International Conference "Random Media"
    • Place of Presentation
      仙台国際センター, 仙台市
    • Year and Date
      2010-01-28
    • Related Report
      2009 Final Research Report
  • [Presentation] Geometric variational problems and bifurcation theory2010

    • Author(s)
      Miyuki Koiso
    • Organizer
      第一回CREST-SBM国際研究集会"Random Media"
    • Place of Presentation
      仙台国際センター(仙台市)
    • Year and Date
      2010-01-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] Variational Problems for Anisotropic Surface Energies2009

    • Author(s)
      Miyuki Koiso
    • Organizer
      第34回偏微分方程式論札幌シンポジウム
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-08-26
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Stability of hypersurfaces with constant mean curvature2009

    • Author(s)
      Miyuki Koiso
    • Organizer
      Differentail Geometry with Mira
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2009-04-15
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Stability of hypersurfaces with constant mean curvature2009

    • Author(s)
      Miyuki Koiso
    • Organizer
      International Conference "Global Analysis and Differential Geometry"
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-03-23
    • Related Report
      2009 Final Research Report
  • [Presentation] Stability of hypersurfaces with constant mean curvature2009

    • Author(s)
      Miyuki Koiso
    • Organizer
      International Conference "Global Analysis and Differential Geometry"
    • Place of Presentation
      佐賀大学理工学部
    • Year and Date
      2009-03-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] Geometry and stability of rotationally symmetric hypersurfaces with constant mean curvature2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      Integrable systems, Geometry and Visualization 2008
    • Place of Presentation
      九州大学
    • Year and Date
      2008-12-11
    • Related Report
      2009 Final Research Report
  • [Presentation] Geometry and stability of rotationally symmetric hypersurfaces with constant mean curvature2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      Integrable systems, Geometry and Visualization 2008
    • Place of Presentation
      九州大学大学院数理学研究院
    • Year and Date
      2008-12-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Anisotropic Gauss map of surfaces2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      One Day workshop on Differential Geometry
    • Place of Presentation
      佐賀大学
    • Year and Date
      2008-11-20
    • Related Report
      2009 Final Research Report
  • [Presentation] Anisotropic Gauss map of surfaces2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      One Day Workshop on Differential Geometry
    • Place of Presentation
      佐賀大学理工学部
    • Year and Date
      2008-11-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] A free boundary problem for surfaces with constant anisotropic mean curvature2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      CONFERENCE Differential Geometry
    • Place of Presentation
      Banach Center at the Mathematical Conference Center Bedlewo, Poland
    • Year and Date
      2008-06-25
    • Related Report
      2009 Final Research Report
  • [Presentation] A free boundary problem for surfaces with constant anisotropic mean curvature2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      CONFERENCE Differential Geometry
    • Place of Presentation
      Banach Center, Bedlewo, Poland
    • Year and Date
      2008-06-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] 非等方的平均曲率一定曲面に対する自由境界問題2008

    • Author(s)
      小磯深幸
    • Organizer
      研究集会「リーマン幾何と幾何解析」
    • Place of Presentation
      筑波大学
    • Year and Date
      2008-02-19
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Presentation] A free boundary problem for surfaces with constant anisotropic mean curvature2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      The 3rd Geometry Conference for Friendship of Japan and China
    • Place of Presentation
      名古屋大学野依記念館
    • Year and Date
      2008-01-28
    • Related Report
      2009 Final Research Report
  • [Presentation] A free boundary problem for surfaces with constant anisotropic mean curvature2008

    • Author(s)
      Miyuki Koiso
    • Organizer
      第3回日中友好幾何学研究集会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2008-01-28
    • Related Report
      2007 Annual Research Report
  • [Presentation] 非等方的平均曲率一定曲面の安定性と一意性について2007

    • Author(s)
      小磯深幸
    • Organizer
      部分多様体論・2007
    • Place of Presentation
      湯沢グランドホテル, 新潟県湯沢町
    • Year and Date
      2007-11-23
    • Related Report
      2009 Final Research Report
  • [Presentation] 非等方的平均曲率一定曲面の安定性と一意性について2007

    • Author(s)
      小磯深幸
    • Organizer
      部分多様体論・2007
    • Place of Presentation
      新潟県湯沢町,湯沢グランドホテル
    • Year and Date
      2007-11-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] 非等方的平均曲率一定曲面の幾何2007

    • Author(s)
      小磯深幸
    • Organizer
      第54回幾何学シンポジウム
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2007-08-24
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Presentation] Geometry of surfaces with constant anisotropic mean curvature2007

    • Author(s)
      Miyuki Koiso
    • Organizer
      Symposium on the differential geometry of submanifolds
    • Place of Presentation
      Valenciennes大学, フランス
    • Year and Date
      2007-07-05
    • Related Report
      2009 Final Research Report
  • [Presentation] Geometry of surfaces with constant anisotropic mean curvature2007

    • Author(s)
      Miyuki Koiso
    • Organizer
      Symposium on the differential geometry of submanifolds
    • Place of Presentation
      Valenciennes大学,フランス
    • Year and Date
      2007-07-05
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.kyushu-u.ac.jp/

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.math.kyushu-u.ac.jp/

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://koto.nara-wu.ac.jp/kenkyu/Profiles/5/0000471/profile.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nara-wu.ac.jp/personal/koiso/koiso.htm#ronbun

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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