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Study on hypersurfaces of constant anisotropic mean curvature with singulalities

Research Project

Project/Area Number 26610016
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionKyushu University

Principal Investigator

KOISO Miyuki  九州大学, マス・フォア・インダストリ研究所, 教授 (10178189)

Co-Investigator(Kenkyū-buntansha) 本多 正平  東北大学, 理学研究科, 准教授 (60574738)
本田 淳史  都城工業高等専門学校, 一般科目理科, 講師 (90708611)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords非等方的エネルギー / ウルフ図形 / 平均曲率一定曲面 / 変分問題 / ローレンツ・ミンコフスキー空間 / ローレンツ多様体 / 離散曲線 / 離散捩率 / 平均曲率 / 非等方的曲面エネルギー / 測度距離空間 / 曲面の特異点
Outline of Final Research Achievements

We studied a mathematical model of small crystals. They are equilibrium surfaces of an anisotropic surface energy which is the integral of the surface tension over the surface. The surface tension depends on the direction of each point of the surface. We derived the condition for a surface to be an equilibrium surface, and we proved the uniqueness of the local energy minimizer for closed plane curves. We also studied a mathematical model of small double crystals, surfaces with constant mean curvature in Lorenz spaces, and curvatures of discrete space curves.

Report

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

    (34 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (7 results) Journal Article (8 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 8 results,  Open Access: 1 results,  Acknowledgement Compliant: 7 results) Presentation (16 results) (of which Int'l Joint Research: 12 results,  Invited: 16 results) Remarks (3 results)

  • [Int'l Joint Research] アイダホ州立大学/ジョージア工科大学(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ピサ高等師範学校(イタリア)

    • Related Report
      2016 Annual Research Report
  • [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] サンパウロ大学(ブラジル)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Idaho State University(米国)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] University of Sao Paulo(ブラジル)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Korea Institute for Advanced Study(韓国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Mixed type surfaces with bounded mean curvature in 3-dimensional space-times2017

    • Author(s)
      A. Honda, M. Koiso, M. Kokubu, M. Umehara and Kotaro Yamada
    • Journal Title

      Diff. Geom. and its Appl.

      Volume: 52 Pages: 64-77

    • DOI

      10.1016/j.difgeo.2017.03.009

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Local spectral convergence in RCD^*(K, N) spaces2017

    • Author(s)
      L. Ambrosio and S.Honda
    • Journal Title

      Nonlinear Analysis

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Duality of singularities for spacelike CMC surfaces2017

    • Author(s)
      A. Honda
    • Journal Title

      Kobe Journal of Mathematics

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Isometric immersions with singularities between space forms of the same positive curvature2017

    • Author(s)
      A. Honda
    • Journal Title

      Journal of Geometric Analysis

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Stable capillary hypersurfaces in a wedge2016

    • Author(s)
      Jaigyoung Choe and Miyuki Koiso
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 280 Issue: 1 Pages: 1-15

    • DOI

      10.2140/pjm.2016.280.1

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space2016

    • Author(s)
      Atsufumi Honda, Miyuki Koiso, and Kentaro Saji
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 未定

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Stability and bifurcation for surfaces with constant mean curvature2016

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

      Journal of the Mathematical Society of Japan

      Volume: 未定

    • NAID

      130006887109

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Bifurcation and symmetry breaking of nodoids with fixed boundary2015

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

      Advances in Calculus of Variations

      Volume: 未定 Issue: 4 Pages: 337-370

    • DOI

      10.1515/acv-2014-0011

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 半正定値計量の幾何学と等長実現問題2017

    • Author(s)
      本田淳史
    • Organizer
      日本数学会2017年度年会幾何学分科会特別講演
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Stability and bifurcation for surfaces with constant mean curvature2017

    • Author(s)
      Miyuki Koiso
    • Organizer
      OIST Mini Symposium: Viscoelasticity and Dissipative Dynamics of Rods and Membranes
    • Place of Presentation
      OIST, Okinawa, Japan
    • Year and Date
      2017-03-07
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability and bifurcation for surfaces with constant mean curvature2017

    • Author(s)
      Miyuki Koiso
    • Organizer
      Southeast Geometry Seminar
    • Place of Presentation
      Georgia Institute of Technology, Atlanta, USA
    • Year and Date
      2017-02-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability and bifurcation for surfaces with constant mean curvature2016

    • Author(s)
      Miyuki Koiso
    • Organizer
      Workshop "Differential Geometry, Lie Theory and Low-Dimensional Topology"
    • Place of Presentation
      La Trobe University, Australia
    • Year and Date
      2016-12-19
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability and bifurcation for surfaces with constant mean curvature2016

    • Author(s)
      Miyuki Koiso
    • Organizer
      Workshop on "Geometric Inequalities on Riemannian Manifolds"
    • Place of Presentation
      Busan, Korea
    • Year and Date
      2016-11-24
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Ricci curvature and Orientability2016

    • Author(s)
      S. Honda
    • Organizer
      Optimal Transport and Applications
    • Place of Presentation
      Scuola Normale Superiore, Italy
    • Year and Date
      2016-11-10
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 曲面に対する非等方的エネルギーの幾何2016

    • Author(s)
      小磯深幸
    • Organizer
      日本数学会2016年度年会,応用数学分科会特別講演
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-18
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Anisotropic surface energy and surfaces with edges2016

    • Author(s)
      Miyuki Koiso
    • Organizer
      Workshop “Transformations and Singularities”
    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan
    • Year and Date
      2016-02-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Local structure of the space of all triply periodic minimal surfaces in R^32015

    • Author(s)
      Miyuki Koiso
    • Organizer
      Geometric aspects on capillary problems and related topics
    • Place of Presentation
      Granada, Spain
    • Year and Date
      2015-12-16
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On bifurcation and local rigidity of triply periodic minimal surfaces in the three-dimensional Euclidean space2015

    • Author(s)
      Miyuki Koiso
    • Organizer
      Workshop “Geometric Analysis in Geometry and Topology 2015”
    • Place of Presentation
      Tokyo University of Science, Tokyo, Japan
    • Year and Date
      2015-11-11
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Local structure of the space of all triply periodic minimal surfaces in R^32015

    • Author(s)
      小磯深幸
    • Organizer
      福岡大学微分幾何研究会
    • Place of Presentation
      福岡大学
    • Year and Date
      2015-10-31
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] On bifurcation and local rigidity of triply periodic minimal surfaces in the three-dimensional Euclidean space2015

    • Author(s)
      Miyuki Koiso
    • Organizer
      8th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Beijing, China
    • Year and Date
      2015-08-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability analysis for surfaces with constant mean curvature2015

    • Author(s)
      Miyuki Koiso
    • Organizer
      Summer School on multiscale and geometric analysis
    • Place of Presentation
      Hokkaido University, Japan
    • Year and Date
      2015-07-29
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability and bifurcation for surfaces with constant mean curvature2015

    • Author(s)
      Miyuki Koiso
    • Organizer
      Singularities in Generic Geometry and its Applications Kobe-Kyoto 2015 (Valencia IV)
    • Place of Presentation
      RIMS, Kyoto University, Japan
    • Year and Date
      2015-06-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Stable capillary hypersurfaces in a wedge and uniqueness of the minimizer2015

    • Author(s)
      Miyuki Koiso
    • Organizer
      Conference “Asymptotic Problems: Elliptic and Parabolic Issues”
    • Place of Presentation
      Vilnius, Lithuania
    • Year and Date
      2015-06-02
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Lorentz-Minkowski空間の空間的CMC曲面の折り目特異点2014

    • Author(s)
      本田淳史
    • Organizer
      第61回幾何学シンポジウム
    • Place of Presentation
      名城大学
    • Year and Date
      2014-08-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Remarks] 九州大学マス・フォア・インダストリ研究所 所員紹介詳細 小磯 深幸/教授

    • URL

      http://www.imi.kyushu-u.ac.jp/academic_staffs/view/86

    • Related Report
      2016 Annual Research Report
  • [Remarks] 九州大学 マス・フォア・インダストリ研究所 所員紹介詳細,小磯 深幸/教授

    • URL

      http://www.imi.kyushu-u.ac.jp/academic_staffs/view/86

    • Related Report
      2015 Research-status Report
  • [Remarks] 研究者情報 小磯深幸

    • URL

      http://hyoka.ofc.kyushu-u.ac.jp/search/details/K003646/index.html

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2022-02-16  

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