GAFA Geometric And Functional Analysis

, Volume 17, Issue 3, pp 936–959

A Combinatorial Model for the Teichmüller Metric

Article

DOI: 10.1007/s00039-007-0615-x

Cite this article as:
Rafi, K. GAFA, Geom. funct. anal. (2007) 17: 936. doi:10.1007/s00039-007-0615-x

Abstract.

We study how the length and the twisting parameter of a curve change along a Teichmüller geodesic. We then use our results to provide a formula for the Teichmüller distance between two hyperbolic metrics on a surface, in terms of the combinatorial complexity of curves of bounded lengths in these two metrics.

Keywords and phrases:

Teichmüller geodesics curve complex quadratic differentials 

AMS Mathematics Subject Classification:

30F60 32G15 57M07 

Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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