On the classification of mapping class actions on Thurston's asymmetric metric
On the classification of mapping class actions on Thurston's asymmetric metric
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DOI：
10.1017/s030500411300039x
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发表时间：
2011-10
影响因子：
0.8
通讯作者：
L. Liu;A. Papadopoulos;W. Su;G. Théret
中科院分区：
文献类型：
--
作者：
L. Liu;A. Papadopoulos;W. Su;G. Théret
本文研究了有限型曲面的映射类群的元素在该曲面的Teichmüller空间上的作用，该空间具有Thurston的非对称度量。我们将这些行动归类为椭圆形，抛物形，双曲和伪双曲，这取决于是否平移距离这样的元素是零或积极的，以及是否达到这个平移距离的值或没有，我们与这四种类型的瑟斯顿的分类映射类元素。这一研究与Bers在Teichmüller空间中用Teichmüller度量所作的研究以及Daskalopoulos和温特沃斯在Teichmüller空间中用Weil-Petersson度量所作的研究是平行的。
Abstract We study the action of the elements of the mapping class group of a surface of finite type on the Teichmüller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic and pseudo-hyperbolic, depending on whether the translation distance of such an element is zero or positive and whether the value of this translation distance is attained or not, and we relate these four types to Thurston's classification of mapping class elements. The study is parallel to the one made by Bers in the setting of Teichmüller space equipped with Teichmüller's metric, and to the one made by Daskalopoulos and Wentworth in the setting of Teichmüller space equipped with the Weil–Petersson metric.