A study of higher dimensional geometric variational problems

2008 Fiscal Year Self-evaluation Report

• Project/Area Number: 18540206
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: ISOBE Takeshi Tokyo Institute of Technology, 大学院・理工学研究科, 准教授 (10262255)
• Project Period (FY): 2006 – 2009
• Keywords: 幾何学的変分問題 / ソボレフ空間 / コンパクト性 / トポロジー

Research Abstract

位相的に非自明な関数空間上定義された、高次元の幾何学的変分問題の解析的な基礎付けを与える。特に関数空間の完備化とその位相的意味を解明する。

Research Products

• [Journal Article] Topological and analytical properties of Sobolev bundles (2009)
  • Author(s): Takeshi Isobe
  • Journal Title: I : the critical case, Annals of Global Analysis and Geometry 35巻 Pages: 277-337
  • Peer Reviewed
• [Journal Article] A regularity result for a class of degenerate Yang-Mills connections in critical dimensions (2008)
  • Author(s): Takeshi Isobe
  • Journal Title: Forum Math 20巻 Pages: 1109-1139
  • Peer Reviewed
• [Journal Article] On a minimizing property of the Hopf soliton in the Faddeev-Skyrme model (2008)
  • Author(s): Takeshi Isobe
  • Journal Title: Rev. Math. Phys. 20巻 Pages: 765-786
  • Peer Reviewed
• [Journal Article] Topology of Sobolev bundles (2007)
  • Author(s): Takeshi Isobe
  • Journal Title: 数理解析研究所講究録 1528巻 Pages: 104-116
  • Peer Reviewed
• [Journal Article] On global singularities of Sobolev mappings (2006)
  • Author(s): Takeshi Isobe
  • Journal Title: Math. Z. 252巻 Pages: 691-730
  • Peer Reviewed
• [Presentation] Topology of Sobolev bundles (2006)
  • Author(s): 磯部健志
  • Organizer: 変分問題とその周辺
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 20060620-20060622