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Bounded combinatorics and the Lipschitz metric on Teichmüller space. (English) Zbl 1254.30075

Summary: Considering the Teichmüller space of a surface equipped with Thurston’s Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these geodesics are cobounded, and that the closest-point projection to these geodesics is strongly contracting. Consequently, these geodesics are stable. Our main tool is to show that one can get a good estimate for the Lipschitz distance by considering the length ratio of finitely many curves.

MSC:

30F60 Teichmüller theory for Riemann surfaces
32Q26 Notions of stability for complex manifolds
32Q05 Negative curvature complex manifolds
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