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n-harmonic maps and geometries of conformal structures on Riemannian manifolds

Research Project

Project/Area Number 15540209
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

NAKAUCHI Nobumitsu  Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (50180237)

Co-Investigator(Kenkyū-buntansha) SHIMA Hirohiko  Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (70028182)
NAITOH Hiroo  Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (10127772)
KAWAI Shigeo  Saga University, Faculty of Culture and Education, Professor, 文化教育学部, 教授 (30186043)
TAKEUCHI Hiroshi  Shikoku University, Faculty of Management and Information Science, Professor, 経営情報学部, 教授 (20197271)
TAKAKUWA Shoichiro  Tokyo Metropolitan University, Faculty of Urban Liberal Arts, Professor, 都市教養学部, 教授 (10183435)
小宮 克弘  山口大学, 理学部, 教授 (00034744)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywordsn-harmonic map / p-harmonic map / variational problem / 共形幾何構造
Research Abstract

In this research, we studied n-harmonic maps and p-harmonic maps. Kawai and Nakauchi gave estimates of Dirichlet p-eigenvalue problems on p-Laplacian using the exponent p and the diameter of source manifolds. In this proof, we utilized, as key lemmas, formulas of Bochner-Weitzenbock type for a certain linear operater, which depends on the exponent p, inplace of the ordinary Bochner technique for the Laplacian. Kawai proved that there exists no L^2-elgen spinor for nonzero eigenvalue on noncompact complete Riemannian manifolds with poles. Takakuwa proved compactness of spaces of harmonic maps and Yang-Mills connections under some conditions.

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (28 results)

All 2005 2004 2003 Other

All Journal Article (19 results) Book (2 results) Publications (7 results)

  • [Journal Article] Symmetric submanifolds associated with irreducible symmetric R-spaces2005

    • Author(s)
      Jurgen Berndt
    • Journal Title

      Mathematische Annalen 332

      Pages: 721-737

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Grassmann geometry on the 3-dimensional Heisenberg group2005

    • Author(s)
      Jun-ichi Inoguchi
    • Journal Title

      Hokkaido Mathematical Journal 34・2

      Pages: 375-391

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Symmetric submanifolds associated with irreducible symmetric R-spaces2005

    • Author(s)
      Jurgen Berndt, Eshenburg, Hiroo Naitoh
    • Journal Title

      Mathematische Annalen 332

      Pages: 721-737

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Grassmann geometry on the 3-dimensional Heisenberg group2005

    • Author(s)
      Jun-ichi Inoguchi, Kenji Kuwabara, Hiroo Naitoh
    • Journal Title

      Hokkaido Mathematical Journal 34

      Pages: 375-391

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The divisibility in the cut-and-paste group of G-manifolds and fibring over the circle within a cobordism class2005

    • Author(s)
      Katsuhiro Komiya
    • Journal Title

      Osaka Journal of Mathematics 42

      Pages: 233-241

    • NAID

      120004844105

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Classification of symmetric submanifolds of symmetric spaces2005

    • Author(s)
      Hiroo Naitoh
    • Journal Title

      Sugaku Exposition (掲載予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The divisibility in the cut-and-paste group of G-manifolds and fibring over the circle within a cobordism class2005

    • Author(s)
      Katsuhiro Komiya
    • Journal Title

      Osaka J.Math. 42

    • NAID

      120004844105

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Intermediate value theorem for functions on classes of Riemann surfaces2005

    • Author(s)
      Makoto Masumoto
    • Journal Title

      Geometric Function Theory in Several Complex Variables (掲載予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Isomorphism classes of algebras with radical cube zero2005

    • Author(s)
      Isao Kikumasa, Hiroshi Yoshimura
    • Journal Title

      The Proceedings of the 4-th China-Japan-Korea International Symposium on Ring Theory

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On some inequalities for capacity in mixed Gaussian channels with feedback2005

    • Author(s)
      Kenjiro Yanagi
    • Journal Title

      Arch.Inequalities and Applications (掲載予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Fundamental properties of Tsallis relative entopy2004

    • Author(s)
      Shigeru Furuich, Kenjiro Yanagi, Ken Kuriyama
    • Journal Title

      J.Math.Phys. 45

      Pages: 4868-4877

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The first eigenvalue of the p-Laplacian on a compact Riemannian manifold2003

    • Author(s)
      Shigeo Kawai
    • Journal Title

      Nonlinear Analysis 55

      Pages: 33-46

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The spectrum of the p-Laplacian and p-harmonic morphisms on graphs2003

    • Author(s)
      Hirshi Takeuchi
    • Journal Title

      Illinois Journal of Math. 47

      Pages: 939-955

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The first eigenvalue of the p-Laplacian on a compact Riemannian manifold2003

    • Author(s)
      Shigeo Kawai, Nobumitsu Nakauchi
    • Journal Title

      Nonlinear Analysis 55

      Pages: 33-46

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The spectrum of the p-Laplacian and p-harmonic morphisms on graphs2003

    • Author(s)
      Hiroshi Takeuchi
    • Journal Title

      Illinois Journal of Math. 47

      Pages: 939-955

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] on the point spectrum of the Dirac operator on a non-compact manifold

    • Author(s)
      Shigeo Kawai
    • Journal Title

      Journal of Geometry and Physics (To appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Geometry of Hessian Structures

    • Author(s)
      Hirohiko Shima
    • Journal Title

      World Scientific (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the point spectrum of the Dirac operator on a non-compact manifold

    • Author(s)
      Shigeo Kawai
    • Journal Title

      Journal of Geometry and Physics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the point spectrum of the Dirac operator on a non-compact manifold

    • Author(s)
      Shigeo Kawai
    • Journal Title

      Journal of Geometry and Physics (To appear)

    • Related Report
      2005 Annual Research Report
  • [Book] Geometry of Hessian Structures2005

    • Author(s)
      Hirohiko Shima
    • Total Pages
      227
    • Related Report
      2004 Annual Research Report
  • [Book] Geometry of Hessian Structures

    • Author(s)
      Hirohiko Shima
    • Total Pages
      238
    • Publisher
      World Scientific
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] Nobumitsu Nakauchi, Shigeo Kawai(共著): "The first eigenvalue of the p-Laplacian on a compact Riemannian manifold"Nonlinear Analysis. 55. 33-46 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroshi Takeuchi: "The spectrum of the p-Laplacian and p-harmonic morphisms on graphs"Illinois Journal of Math.. 47. 939-955 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Katsuhiro Komiya: "Cutting and pasting of manifolds into G-manifolds"Kodai Math.J.. 26. 230-243 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Katsuhiro Komiya: "Cutting and pasting of families of submanifolds modeled on Z_2-mamifolds"Tokyo J.Math.. 26. 403-411 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroo Naitoh, Jun-ichi Inoguchi, Kenji Kuwabara(共著): "Grassmann geometry on the 3-dimensional Heisenberg group"Hokkaido Mathematical Journal. (掲載予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] Kenjiro Yanagi: "On some inequalities for capacity in mixed Gaussian channels with feedback"Arch.Inequalities and Applications. (掲載予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] 高桑昇一郎: "微分方程式と変分法"共立出版. 163 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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