COARSE AND FINE GEOMETRY OF THE THURSTON METRIC

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-p...

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Bibliographic Details
Published in:Forum of mathematics. Sigma 2020, Vol.8, Article e28
Main Authors: DUMAS, DAVID, LENZHEN, ANNA, RAFI, KASRA, TAO, JING
Format: Article
Language:English
Subjects:
30F60
57M50
Geodesy
Geometry
Toruses
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Summary: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.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2020.3