Problems on the Thurston metric

2015 ◽  
pp. 55-72
Author(s):  
Weixu Su
Keyword(s):  
Thurston Metric

scholarly journals COARSE AND FINE GEOMETRY OF THE THURSTON METRIC

2020 ◽  
Vol 8 ◽  
Author(s):  
DAVID DUMAS ◽  
ANNA LENZHEN ◽  
KASRA RAFI ◽  
JING TAO
Keyword(s):  
Finite Type ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Global Behavior ◽  
Coarse Geometry ◽  
Hyperbolic Structures ◽  
Punctured Torus ◽  
Thurston Metric ◽  
Detailed Picture

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.

scholarly journals The Thurston Metric on Hyperbolic Domains and Boundaries of Convex Hulls

2010 ◽  
Vol 20 (6) ◽  
pp. 1317-1353
Author(s):  
Martin Bridgeman ◽  
Richard D. Canary
Keyword(s):  
Convex Hulls ◽  
Thurston Metric ◽  
Hyperbolic Domains
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