2003 Fiscal Year Final Research Report Summary
Research on rigidity and finiteness for holomorphic mappings on complex hyperbolic manifolds
| Project/Area Number |
13640156
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Tokyo Institute of Technology |
|---|
Principal Investigator |
SHIGA Hiroshige Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (10154189)
|
|---|
| 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)
|
|---|
| Project Period (FY) |
2001 – 2003
|
| Keywords | Hyperbolic Manifold / Fuchsian group / Complex dynamics |
|---|
| 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.
|
