2005 Fiscal Year Final Research Report Summary
Study of Conformal Geometry and Group C^*-bundle from the Viewpoint of Global Analysis
| Project/Area Number |
16540059
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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 |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
AKUTAGAWA Kazuo Tokyo University of Science, Faculty of Science and Technology, Professor, 理工学部, 教授 (80192920)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Osamu Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (10153595)
MORIYOSHI Hitoshi Keio University, Faculty of Science and Technology, Associate Professor, 理工学部, 助教授 (00239708)
KUMURA Hironori Shizuoka University, Faculty of Science, Associate Professor, 理学部, 助教授 (30283336)
TONEGAWA Yoshihiro Hokkaido University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (80296748)
IZEKI Hiroyasu Tohoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90244409)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Differential Geometry / Conformal Geometry / Yamabe Invariant / Laplace Operator / Non-linear Analysis / Inverse Mean Curvature Flow / Discrete Group / Harmonic Map |
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| Research Abstract |
We have studied the following :
(1)Study of Yamabe Invariants
We estimated and determined the Yamabe invariant of some positive 3-manifolds, by using the inverse mean curvature flow and families of Green's functions. In especial, we classified completely all 3-manifolds with Yamabe invariant greater than that of RP^3. We also studied the positive Yamabe constants of Riemannian products and the behavior of them under magnifying one factor. We are now studying Aubin's type lemma for the positive Yamabe constants of infinite coverings, with some new results.
(2)Study of Conformal/Affine Geometry and group C^*-algebra
We gave new developments on conformal and projective geometry. In particular, we obtained an interesting varitional characterization of affine connections induced from Einstein metrics. We studied on twisted K-theory and groupoid C^*-algebras, and then proved a generalization of Gromov-Lawson theorem for foliated spaces.
(3)Study on Non-linear Analysis in Geometry
We studied on eigenvalue problem on complete manifolds, discrete groups and valiational problems on mean curvature. We then obtained results on non-existence of eigenvalues on complete manifolds of non-positive curvature, and a fixed-point theorem for discrete-group actions on Hadamard spaces.
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Research Products
(10 results)
