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- Title
COARSE AND FINE GEOMETRY OF THE THURSTON METRIC.
- Authors
DUMAS, DAVID; LENZHEN, ANNA; RAFI, KASRA; TAO, JING
- Abstract
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.
- Subjects
METRIC geometry; METRIC spaces; TEICHMULLER spaces; HYPERBOLIC spaces; HYPERBOLOID structures
- Publication
Forum of Mathematics, Sigma, 2020, Vol 8, p1
- ISSN
2050-5094
- Publication type
Article
- DOI
10.1017/fms.2020.3