1986 Fiscal Year Final Research Report Summary
Complex analysis and analytic manifolds
| Project/Area Number |
60302004
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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 | TOHOKU UNIVERSITY |
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Principal Investigator |
KURODA Tadashi Tohoku University, Faculty of Science, professor, 理学部, 教授 (40004238)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIMOTO Hirotaka Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (60023595)
IKEGAMI Teruo Osaka Cit 大阪市立大学, 理学部, 教授 (90046889)
SUITA Nobuyuki Tokyo Institute of Technology, Faculty of Science, Professor, 理学部, 教授 (90016022)
MATSUMOTO Kikuji Nagoya University, Department of General Education, Professor, 教養部, 教授 (90023522)
TANIGUCHI Masahiko Kyoto University, Faculty of Science, Associate Professor, 理学部, 助教授 (50108974)
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| Project Period (FY) |
1985 – 1986
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| Keywords | algebroid functions / Douglas algebra / potential / Caratheodory hyperbolic manifolds / Douady spaces / ベルグマン計量 |
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| Research Abstract |
To proceed the study of complex analysis and analytic manifolds, we dealt with the fundamental research of conformal mappings, potential theory, Teichmuller spaces and analytic functions of several complex variables.
As the fundamental research of conformal mappings, we took up a problem on analytic mappings between Riemann surfaces of algebroid functions and could get a fine result on the problem. Furthermore, we succeeded to grasp the meaning of Douglas algebra of bounded functions.
In the research of potential theory, the potential with function kernels were discussed and conditions for a certain kernel to be the resolvent kernel were obtained.
As studies on Teichmuller spaces, we could find a new meaning of classifications of holomorphic automorphisms of a Riemann surface due to Bers and Thurston. Moreover, a study on the Douady space of holomorphic mappings of a closed Riemann surface into a two dimensional closed hyperbolic manifold in the sense of Caratheodory was developped.
As the research on analytic functions of several variables, we could obtain the characterizations of symmetric domains by using eigenvalues of the curvature operator of Bergman metric and succeeded also to get a result on the finiteness theorem on meromorphic mappings into complex projective spaces.
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Research Products
(28 results)
