1991 Fiscal Year Final Research Report Summary
Problems in the Global analysis
| Project/Area Number |
02452004
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Keio University |
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Principal Investigator |
OBATA Morio Keio University Professor, 理工学部, 教授 (90087015)
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| Co-Investigator(Kenkyū-buntansha) |
MAEDA Yoshiaki Keio University Associate Professor, 理工学部, 助教授 (40101076)
前島 信 慶応義塾大学, 理工学部, 教授 (90051846)
ITO Yuji Keio University Professor, 理工学部, 教授 (90112987)
TANAKA Hiroshi Keio University Professor, 理工学部, 教授 (70011468)
菊池 紀夫 慶応義塾大学, 理工学部, 教授 (80090041)
ISHII Ippei Keio University Associate Professor (90051929)
KANAI Masahiko Keio University Assistant Professor (70183035)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Yang-Mills fields / Harmonic maps / stability for the variational problem / operator algebra / self-similarity / fractals / knot theory / Markov process |
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| Research Abstract |
Through 1991 year, we invited. many researchers from the wide subjects in mathematics to ge+ new informations and current results. We arranged seminars and discuss with them mainly at Keio University. Throughtout the discussions, some results have been made by coorperators in our group of this projects. Namely, the existence of the global weak solutions for the YangMills gradient flow and the variational problems for the Harmaonic maps were studied by Maeda, Kikuch and Tani. They established the basic problems and could get-affirmative answers. Now, they are going to study these in more details. Kanai and Nakada got some results on the problems on the number theory and the rigidity of the group actions on non-positive manifolds from the ergodic theoretical points of view. Ishii is given some topological invariants for 3-manifolds by the study of knots and links. Tanaka gives the new ideas for studying the properties on manifolds by using the stochastic analysis.
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