1996 Fiscal Year Final Research Report Summary
Analysis and Applications of Teichmuller space
| Project/Area Number |
08454026
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
TANIGUCHI Masahiko Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50108974)
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| Co-Investigator(Kenkyū-buntansha) |
SUGAWA Toshiyuki Kyoto Univ., Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (30235858)
KOKUBU Hiroshi Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50202057)
OKAJI Takashi Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (20160426)
NOMURA Takaaki Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30135511)
HIRAI Takeshi Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70025310)
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| Project Period (FY) |
1996
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| Keywords | Teichmuller space / Complex dynamics / Kleinian groups / Quasiconformal map / Riemann surface / Fractal sets / Julia sets / Hausdorff dimension |
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| Research Abstract |
The results can be devided into two categories ; those on the Teichmuller spaces and those on objects which provide the Teichmuller spaces. Among oter things, the research on the Teichmuller spaces of infinite dimension is very important.
The Head investigator Taniguchi has clarified the fundamental structures of the Teichmuller space of a transcendental entire function, including the relationship between the absence of wandering domains and finite dimensionality of the corresponding Teichmuller space. These results are the coproduct with T.Harada, a graduate student, and very important, for they give a new light for the investigations on the complex dynamics induced by transcendental entire functions as in the cases of rational functions and of Kleinian groups.
Also Taniguchi has investigated the coiling property, appeared only in the case of infinite dimension, and proved that the Bloch convergence on the universal Teichmuller space is equivalent to Caratheodory convergence, when we consider points of the universal teichmuller space as fractal sets on the plane.
Next, a crucial divice for the Teichmuller theory is a quasiconformal map. Investigator Sugawa has suceeded to give a characterization of the Teichmuller spaces of finite Riemann surfaces without cusps. Sugawa has also given quantative estimate on domain constants related to uniform perfectness. As a consequence, we have interesting estimates of the Hausdorff dimensions of the Julia sets of a complex dynamics, or of the limit set of a Kleinian group.
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