GAFA Geometric And Functional Analysis

, Volume 17, Issue 3, pp 936-959

First online:

A Combinatorial Model for the Teichmüller Metric

  • Kasra RafiAffiliated withDepartment of Mathematics, University of Chicago Email author 

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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