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New methods on geometric analysis of variational problems for surfaces

Research Project

Project/Area Number 25287012
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
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) 庄田 敏宏  佐賀大学, 文化教育学部, 准教授 (10432957)
川上 裕  金沢大学, 数物科学系, 准教授 (60532356)
小野寺 有紹  九州大学, マス・フォア・インダストリ研究所, 助教 (70614999)
Co-Investigator(Renkei-kenkyūsha) CHENG Qing-Ming  福岡大学, 理学部, 教授 (50274577)
MIYAMOTO Umpei  秋田県立大学, 総合科学教育研究センター, 准教授 (70386621)
EJIRI Norio  名城大学, 理工学部, 教授 (80145656)
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥10,790,000 (Direct Cost: ¥8,300,000、Indirect Cost: ¥2,490,000)
Fiscal Year 2016: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywords平均曲率一定曲面 / 極小曲面 / 安定性 / 変分問題 / 分岐理論 / 三重周期極小曲面 / 自由境界問題 / プラトー問題 / 平均曲率 / 曲面の安定性 / 非等方的曲面エネルギー / ガウス写像 / 幾何学 / 国際研究者交流(米国:ブラジル) / 国際研究者交流(ブラジル:韓国) / 国際情報交換(米国)
Outline of Final Research Achievements

Under given boundary conditions, minimal surfaces are critical points of area, and surfaces with constant mean curvature (CMC surfaces) are critical points of area among surfaces enclosing the same volume. Such a surface is said to be stable if it attains a local minimum of area for all admissible variations. In this research, we studied criteria for stability, existence and uniqueness of (stable) critical points, bifurcation of critical points, for fixed, free, and periodic boundary conditions.

Report

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

    (52 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (6 results) Journal Article (11 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 10 results,  Open Access: 1 results,  Acknowledgement Compliant: 8 results) Presentation (28 results) (of which Int'l Joint Research: 13 results,  Invited: 28 results) Book (2 results) Remarks (4 results) Funded Workshop (1 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] フィレンツェ大学(イタリア)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] 国立ハノイ教育大学(ベトナム)

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

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

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

    • Related Report
      2015 Annual Research 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] A note on a unicity theorem for the Gauss maps2017

    • Author(s)
      Pham Hoang Ha, Yu Kawakami
    • Journal Title

      Canadian Mathematical Bulletin

      Volume: 印刷中 Issue: 2 Pages: 292-300

    • DOI

      10.4153/cmb-2017-015-0

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / 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] Dynamical approach to an overdetermined problem in potential theory2016

    • Author(s)
      Michiaki Onodera
    • Journal Title

      J. Math. Pures Appl.

      Volume: 未定 Issue: 4 Pages: 768-796

    • DOI

      10.1016/j.matpur.2016.03.011

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

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

      Pacific Journal of Mathematics

      Volume: 282 Pages: 107-144

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research Report 2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Stability of hypersurfaces with constant mean curvature and applications to isoperimetric problems2013

    • Author(s)
      Miyuki Koiso
    • Journal Title

      RIMS Kokyuroku

      Volume: 1850 Pages: 23-33

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Stable surfaces with constant anisotropic mean curvature and circular boundary2013

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

      Proceedings of the American Mathematical Society

      Volume: 141 Issue: 11 Pages: 3817-3823

    • DOI

      10.1090/s0002-9939-2013-11892-7

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] On the solution structure of Bernoulli's free boundary problem2017

    • Author(s)
      M. Onodera
    • Organizer
      The 9th Nagoya Workshop on Differential Equations
    • Place of Presentation
      名古屋大学
    • Year and Date
      2017-03-22
    • 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
      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] Dynamical approach to an overdetermined problem2016

    • Author(s)
      M. Onodera
    • Organizer
      Korea-Japan International Workshop of Nonlinear Partial Differential Equations --- Aspect of Regularity and Asymptotics ---
    • Place of Presentation
      洞爺サンパレス
    • Year and Date
      2016-11-18
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 完備極小曲面のガウス写像の値分布論的性質の幾何学的解釈について2016

    • Author(s)
      川上裕
    • Organizer
      2016年度日本数学会秋季総合分科会函数論分科会特別講演
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
    • 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 効率の良い形は美しいか? --- 曲面の変分問題と応用 ---2014

    • Author(s)
      小磯深幸
    • Organizer
      九 州大学テクノロジーフォーラム2014
    • Place of Presentation
      東京国際フォーラム
    • Year and Date
      2014-12-03
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 3次元ユークリッド空間内の三重周期極小曲面の剛性・分岐・共 連続構造への応用2014

    • Author(s)
      小磯深幸
    • Organizer
      日本応用数理学会2014 年度年会
    • Place of Presentation
      政策研究大学院大学
    • Year and Date
      2014-09-04
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 3次元ユークリッド空間内の三重周期極小曲面の剛性と分岐につ いて2014

    • Author(s)
      小磯深幸
    • Organizer
      第61回幾何学シンポジウム
    • Place of Presentation
      名城大学
    • Year and Date
      2014-08-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On bifurcation and local rigidity of triply periodic minimal surfaces in R^32014

    • Author(s)
      Miyuki Koiso
    • Organizer
      5th International Workshop on Differential Geometry and Analysis
    • Place of Presentation
      Karatsu, Japan
    • Year and Date
      2014-06-03
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Bernstein-type theorems for surfaces with constant anisotropic mean curvature and CMC surfaces in the Lorentz-Minkowski space

    • Author(s)
      Miyuki Koiso
    • Organizer
      7th International Meeting on Lorentzian Geometry
    • Place of Presentation
      Sao Paulo, Brazil
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Free boundary problem for surfaces with constant mean curvature

    • Author(s)
      Miyuki Koiso
    • Organizer
      International Workshop on Special Geometry and Minimal Submanifolds
    • Place of Presentation
      Tohoku University, Japan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 曲面の変分問題の解の安定性 --- 判定法と応用.極小曲面と平均曲率一定曲面を中心に ---

    • Author(s)
      小磯深幸
    • Organizer
      山口幾何学研究集会2013 --- 進化する曲面論 ---
    • Place of Presentation
      山口大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Geometry of hypersurfaces with constant anisotropic mean curvature

    • Author(s)
      Miyuki Koiso
    • Organizer
      The 2013 Annual Meeting of the Taiwan Mathematical Society
    • Place of Presentation
      National Sun Yat-sen University, Taiwan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Stable capillary hypersurfaces in a wedge and uniqueness of the minimizer

    • Author(s)
      Miyuki Koiso
    • Organizer
      The second Japanese-Spanish workshop on Differential Geometry
    • Place of Presentation
      Tokyo Institute of Technology, Japan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 非等方的平均曲率一定曲面に対するバランス公式とその応用

    • Author(s)
      小磯深幸
    • Organizer
      福岡大学幾何学研究会
    • Place of Presentation
      福岡大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Balancing formula for immersed hypersurfaces with constant anisotropic mean curvature and its applications

    • Author(s)
      Miyuki Koiso
    • Organizer
      名城大学幾何学研究集会 "Progress of geometric structures on manifolds"
    • Place of Presentation
      名城大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Bifurcation theory for minimal and constant mean curvature surfaces

    • Author(s)
      Miyuki Koiso
    • Organizer
      Conference on Geometry
    • Place of Presentation
      Galatasaray University, Istanbul, Turkey
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Book] A Mathematical Approach to Research Problems of Science and Technology - Theoretical Basis and Developments in Mathematical Modeling2014

    • Author(s)
      Ryuei Nishii 他
    • Total Pages
      507
    • Publisher
      Springer
    • Related Report
      2014 Annual Research Report
  • [Book] A Mathematical Approach to Research Problems of Science and Technology - Theoretical Basis and Developments in Mathematical Modeling2014

    • Author(s)
      Ryuei Nishii, Shin-ichiro Ei, Miyuki Koiso, Hiroyuki Ochiai, Kanzo Okada, Shingo Saito, Tomoyuki Shirai, 他.
    • Total Pages
      400
    • Publisher
      Springer
    • Related Report
      2013 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
      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 Annual Research 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 Annual Research Report
  • [Remarks] マス・フォア・インダストリ研究所 所員紹介詳細 小磯深幸

    • URL

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

    • Related Report
      2013 Annual Research Report
  • [Funded Workshop] The First Japan-Taiwan Joint Conference on Differential Geometry2016

    • Place of Presentation
      早稲田大学 西早稲田キャンバス 63号館2階第三会議室
    • Year and Date
      2016-12-13
    • Related Report
      2016 Annual Research Report

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Published: 2013-05-21   Modified: 2022-02-16  

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