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A characterization of short curves of a Teichmüller geodesic. (English) Zbl 1082.30037
In this paper, the author obtains a combinatorial condition to characterize short curves along a Teichmüller geodesic. This condition is similar to the one given by Minsky for a hyperbolic 3-manifold. He shows that short curves in a hyperbolic manifold homeomorphic to \(S\times R\) are also short in the corresponding Teichmüller geodesic, and he provides examples demonstrating that its converse is false.

30F60 Teichmüller theory for Riemann surfaces
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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[4] M Rees, The geometric model and large Lipschitz equivalence direct from Teichmüller geodesic, preprint · www.liv.ac.uk
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