Analysis and Applications of Teichmuller space

Teichmuller空间的分析与应用

基本信息

批准号：
08454026
负责人：
TANIGUCHI Masahiko
金额：
$ 4.54万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至无数据
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08454026/
关键词：
Teichmuller space Complex dynamics Kleinian groups Quasiconformal map Riemann surface Fractal sets Julia sets Hausdorff dimension

项目摘要

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.

结果可以分为两类。 Teichmuller空间和提供Teichmuller空间的物体上的那些。在OTER的事物中，关于无限维度的Teichmuller空间的研究非常重要。主管Taniguchi阐明了超越整个功能的Teichmuller空间的基本结构，包括缺乏徘徊领域的缺乏与有限范围的关系之间的关系。相应的Teichmuller空间。这些结果是与研究生T.Harada的副作用，非常重要，因为它们为对先验全部功能引起的复杂动力学的研究提供了新的启示，就像在有理功能和kleinian群体的情况下一样。已经研究了盘绕特性，仅在无限维度的情况下出现，并证明了通用teichmuller空间上的Bloch收敛性等于Caratheodory Contrangence，当我们考虑通用Teichmuller空间的点作为平面上的分形集合。 Teichmuller理论的关键划分是一张准文化图。 Sugawa的研究者已成功地描述了有限的Riemann表面的Teichmuller空间，而没有尖端。 Sugawa还对与统一完美相关的域常数进行了量化估计。结果，我们对复杂动力学的朱莉亚集合或克莱尼群的极限集的豪斯多夫尺寸进行了有趣的估计。