Some metrics on Teichmüller spaces of surfaces of infinite type
Some metrics on Teichmüller spaces of surfaces of infinite type
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DOI：
10.1090/s0002-9947-2011-05090-7
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发表时间：
2008-08
影响因子：
1.3
通讯作者：
Li-Xing Liu;A. Papadopoulos
中科院分区：
文献类型：
--
作者：
Li-Xing Liu;A. Papadopoulos
与拓扑有限类型的曲面不同，拓扑无限类型的曲面有几个不同的Teichmuller空间。这些Teichmuller空间首先取决于我们是在双曲范畴中工作还是在共形范畴中工作。在给定视点(双曲或圆锥)的情况下，它们还取决于Teichmuller空间上距离函数的选择。在双曲设置中自然出现的距离函数的例子有长度谱距离和双Lipschitz距离，还有其他有用的距离函数。TeichMuller空间还取决于基点的选择。本文的目的是给出有限类型曲面的TeichMuller理论中没有出现的无限拓扑型曲面的TeichMuller理论的一些例子、结果和问题。特别地，我们指出了与给定的拓扑无限型曲面相关的各种TeichMuller空间之间的联系和区别。AMS数学学科分类：32G15；30F30；30F60。
Unlike the case of surfaces of topologically finite type, there are several different Teichmuller spaces that are associated to a surface of topo- logical infinite type. These Teichmuller spaces first depend (set-theoretically) on whether we work in the hyperbolic category or in the conformal category. They also depend, given the choice of a point of view (hyperbolic or confor- mal), on the choice of a distance function on Teichmuller space. Examples of distance functions that appear naturally in the hyperbolic setting are the length spectrum distance and the bi-Lipschitz distance, and there are other useful distance functions. The Teichmuller spaces also depend on the choice of a basepoint. The aim of this paper is to present some examples, results and questions on the Teichmuller theory of surfaces of infinite topological type that do not appear in the setting the Teichmuller theory of surfaces of finite type. In particular, we point out relations and differences between the various Teichmuller spaces associated to a given surface of topological infinite type. AMS Mathematics Subject Classification: 32G15 ; 30F30 ; 30F60.