| Project/Area Number |
13640156
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Tokyo Institute of Technology |
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Principal Investigator |
SHIGA Hiroshige Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (10154189)
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| Co-Investigator(Kenkyū-buntansha) |
SUMI Hiroki Tokyo Institute of Technology, Department of Mathematics, Assistant Professor, 大学院・理工学研究科, 助手 (40313324)
TANABE Masaharu Tokyo Institute of Technology, Department of Mathematics, Assistant Professor, 大学院・理工学研究科, 助手 (60272663)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | Hyperbolic Manifold / Fuchsian group / Complex dynamics / ファック群 |
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| Research Abstract |
We consider holomorphic mappings from an m-dimensional complex hyperbolic manifold M to an n-dimensional complex manifold N represented by a quotient space of a bounded domain N' of the complex space via a discrete automorphism group of N'. We show that if M is of divergence type, then the dimension of the space of the holomorphic mappings from M to N is bounded by the essential boundary dimension of N'. In particular, we may show a finiteness theorem for dominant holomorphic mappings from M to N. We also consider holomorphic mappings on compact Riemann surfaces and their dynamics.
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