Geodesic
COARSE AND FINE GEOMETRY OF THE THURSTON METRIC
Forum of Mathematics, Sigma, Tome 8 (2020)

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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. 
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     author = {DAVID DUMAS and ANNA LENZHEN and KASRA RAFI and JING TAO},
     title = {COARSE {AND} {FINE} {GEOMETRY} {OF} {THE} {THURSTON} {METRIC}},
     journal = {Forum of Mathematics, Sigma},
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DAVID DUMAS; ANNA LENZHEN; KASRA RAFI; JING TAO. COARSE AND FINE GEOMETRY OF THE THURSTON METRIC. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.3

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