1996 Fiscal Year Final Research Report Summary
Research on Complex Manifolds and Complex Analysis
| Project/Area Number |
07304063
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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 | 総合 |
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| Research Field |
解析学
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| Research Institution | Shizuoka University |
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Principal Investigator |
SATO Hiroki Shizuoka Univ., Fac.of Sci., Dept.of Math., Professor, 理学部, 教授 (40022222)
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| Co-Investigator(Kenkyū-buntansha) |
WATANABE Hisako Ochanomizu Univ., Fac.of Sci., Dept.of Math., Professor, 理学部, 教授 (70017193)
IMAYOSHI Yoichi City Univ.of Osaka, Fac.of Sci., Dept.of Math., Professor, 理学部, 教授 (30091656)
FUJIMOTO Hirotaka Kanazawa Univ., Fac.of Sci., Dept.of Math., Professor, 理学部, 教授 (60023595)
TODA Nobushige Nagoya Institute of Technology, Fac.of Tech., Professor, 工学部, 教授 (30004295)
TANIGUCHI Masahiko Kyoto Univ., Graduade School of Sci., Dept of Math., Associate Professor, 大学院・理学研究科, 助教授 (50108974)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Schottky group / Kleinian group / Teichmuller space / Value distribution theory / Riemann surface / Complex manifold / Conformal mapping / Potential theory |
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| Research Abstract |
Head investigator, H.Sato studied the following. 1.He represented the shape of all eight kinds of classical Schottky spaces of real type and found generators for the Schottky modular groups acting on the spaces and determined fundamental regions for the Schottky modular groups. The results have been submitted as a paper titled on "Classical Schottky groups of real type of genus two, III" . 2.He gives the best lower bounds of Jorgensen's numbers for classical Schottky groups of real type. The results have been submitted as a paper titled on "Jogensen's inequality for classical Schottky groups of real type " . Furthermore he obtained some results on the Hausdorff dimensions of the limit set of Fuchsian Schottky groups.
M.Taniguchi showed the equivalence of the convergence in the Bloch norm and the geometric convergence in the sense of Caratheodory. H.Fujimoto extended the Nevanlinna theory for minimal surfaces due to Beckenbach to the case of the minimal surfaces for parabolic Riemann surfaces. Y.Imayoshi estimated the number of non-constant holomorphic mappings between closed Riemann surfaces by the genus of the surfaces. N.Toda investigated the second fundamental theorem, defect relation of holomorphic curves on the complex plane and inproved the results obtained by H.Cartan. H.Yoshida obtained some results on the uniqueness theorem of the solutions of Dirichlet problem in unbounded domains. H.Watanabe defined and studied the double layr potentials for a bounded domain with fractal boundary.
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