2002 Fiscal Year Final Research Report Summary
Geometric researches in complex analysis
| Project/Area Number |
12304007
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
FUJIMOTO Hirotaka Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (60023595)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAGUCHI Hiroshi Nara Woman University, Faculty of Science, Professor, 理学部, 教授 (20025406)
UEDA Tetsuo Kyoto University, Faculty of Integrated Human Studies, Professor, 総合人間学部, 教授 (10127053)
MORI Seiki Yamagata University, Faculty of Science, Professor, 理学部, 教授 (80004456)
SATO Hiroshi Shizuoka University, Faculty of Science, Professor, 理学部, 教授 (40022222)
SHIBA Masakazu Hiroshima University, Faculty of Engineering, Professor, 工学部, 教授 (70025469)
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| Project Period (FY) |
2000 – 2002
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| Keywords | hyperbolic manifold / value distribution theory / holomorphic mapping / uniqueness theorem / defect / holomorphic automorphism group / complex dynamics / complex differential equation |
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| Research Abstract |
The purpose of this research is to investigate complex analysis in the aspect of geometry and, moreover, to give applications of complex analysis to geometry. To these ends, we need to have interchanges of researchers in various fields of mathematics. We held various sympsiums many times and obtained many new results in these fields.
H. Fujimoto succeeded in the constructions of hyperbolic hypersurfaces of degree 2^n in the n (【greater than or equal】3)-dimensional complex projective space. He also obtained some sufficient conditions for polynomials to be uniqueness polynomials. S. Mori, together with Y. Aihara, constructed many examples of holomorphic mappings into the complex projective space with pre-assinged positive deficiency. T. Ueda studied fixed points of polynomial automorphisms of C^n and showed that the sum of holomorphic Lefshetz indices vanishes for generalized Henon maps under some conditions. By introducing the notion of balayage vector potentials, H. Yamaguchi maked clear the importance of harmonic forms. H. Sato founded many kinds of Jorgensen groups. H. Kazama studied complex analytic cohomology groups of topologically trivial line bundles over 1-dimension complex torus and showed the existence of formal Hartogs-Laurent series associated with line bundles. A. Kodama investigated the conditions for domains whose boundary are strongly pseudo-convex excluding some singularities to become complete Riemannian manifolds with respect to Webster me trices.
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