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Article Dans Une Revue Geometriae Dedicata Année : 2012

Bounded combinatorics and the Lipschitz metric on Teichmüller space

Résumé

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.

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Dates et versions

hal-00695587 , version 1 (09-05-2012)

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Anna Lenzhen, Kasra Rafi, Jing Tao. Bounded combinatorics and the Lipschitz metric on Teichmüller space. Geometriae Dedicata, 2012, 159, pp.353-371. ⟨10.1007/s.10711-011-9664-2⟩. ⟨hal-00695587⟩
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