A Combinatorial Model for the Teichmüller Metric
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- Rafi, K. GAFA, Geom. funct. anal. (2007) 17: 936. doi:10.1007/s00039-007-0615-x
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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.