1988 Fiscal Year Final Research Report Summary
Analysis on Complex Manifold
| Project/Area Number |
62302003
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | TOKYO INSTITUT OF TECHNOLOGY |
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Principal Investigator |
NOGUCHI Junjiro Faculty of Science, Tokyo Institut of Technology, 理学部, 教授 (20033920)
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| Co-Investigator(Kenkyū-buntansha) |
KAZAMA Hideki College of General Education, Kyushu University, 教養部, 助教授 (10037252)
TANIGUCHI Masahiko Faculty of Science, Kyoto University, 理学部, 助教授 (50108974)
IMAYOSHI Yoichi College of General Education, Osaka University, 教養部, 助教授 (30091656)
ITO Masayuki College of General Education, Nagoya University, 教養部, 教授 (60022638)
SUITA Nobuyuki Faculty of Science, Tokyo Institut of Technology, 理学部, 教授 (90016022)
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| Project Period (FY) |
1987 – 1988
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| Keywords | complex analysis / complex manifold / potential theory / Riemann surface / several complex variables / holomorphic function / hyperbolic manifold / 正則関数 |
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| Research Abstract |
There are a number of outstanding results obtained under the present project and thus the aim of the project is thought to be fulfilled. One of those results is due to H.Fujimoto: He finally solved the so-called Gauss map conjecture (1961). It asserts that there are at most 4 exceptional values of the Gauss map of a complete non-fiat minimal surface in the real 3-dimensional euclidean space. He received the 1988 Geometry Prize (Japan Math. Soc.) for this work. It has been a big problem to extend a L^2 holomorphic function defined on a submanifold of a stein manifold to the whole space as L^2 holmorphic functions. T.Ohsawa solved this problem even with norm estimate. He also obtained an isomorphism theorem between the intersection and the L^2 cohomologies, and moreover established the Hodge theory on pseudoconvex Kahler manifolds (with I. Takegoshi). J.Noguchi proved the extension-convergence theorem for sequences of holomorphic mappings into a hyperbolic space anded it to obtain precise structure theorems of the moduli spaces of holomorphic mappings the results have application to the diophantus geometry over function fields and answer a few problems posed by S.Lang and other. T.Murai deepened the sutdy of analytic capacity, and solved the Vitushkin conhecture in the joint work with P.Jones. Based on works of Fricke and Weil, K.Saito found a new method to construct the Teichmuller space, which carries a canonical structure of S^1-bundle and ample group theoretical structure. It is hoped the researchs of the present project will be more actively studied and develop.
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Research Products
(14 results)
