COARSE AND FINE GEOMETRY OF THE THURSTON METRIC
COARSE AND FINE GEOMETRY OF THE THURSTON METRIC
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DOI：
10.1017/fms.2020.3
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发表时间：
2016-10
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影响因子：
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通讯作者：
D. Dumas;Anna Lenzhen;Kasra Rafi;Jing Tao
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作者：
D. Dumas;Anna Lenzhen;Kasra Rafi;Jing Tao
本文研究了曲面上双曲结构的Teichmüler空间上的瑟斯顿度量的几何性质。我们关于这一度量的粗几何的一些结果适用于有限类型的任意曲面$S$；然而，我们特别关注曲面是一次穿孔环面的情况。在这种情况下，我们的结果提供了瑟斯顿度规的测地线的无穷小、局部和全局行为的详细图景，以及罗登定理的类似。
We study the geometry of the Thurston metric on the Teichmüller space of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type; however, we focus particular attention on the case where the surface is a once-punctured torus. In that case, our results provide a detailed picture of the infinitesimal, local, and global behavior of the geodesics of the Thurston metric, as well as an analogue of Royden’s theorem.