2005 Fiscal Year Final Research Report Summary
n-harmonic maps and geometries of conformal structures on Riemannian manifolds
| Project/Area Number |
15540209
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Yamaguchi University |
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Principal Investigator |
NAKAUCHI Nobumitsu Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (50180237)
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| 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)
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| Project Period (FY) |
2003 – 2005
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| Keywords | n-harmonic map / p-harmonic map / variational problem |
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| 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.
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