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hal-00129729, version 1

On Teichmueller's metric and Thurston's asymmetric metric on Teichmueller space

Athanase Papadopoulos 1, Guillaume Théret 1

(06/07/2006)

Résumé : We review some elements of Teichmueller's metric and of Thurston's asymmetric metric on Teichmueller space. One of our objectives is to draw a parallel between these two metrics and to stress on some differences between them. The results that we present on Teichmueller's metric are classical, whereas some of the results on Thurston's asymmetric metric are new. We also discuss some open problems.

  • 1 :  Institut de Recherche Mathématique Avancée (IRMA)
  • CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I
  • Domaine : Mathématiques/Variables complexes
  • Mots-clés : "conformal structure – Riemann surface – hyperbolic structure – Teichmueller space – Teichmueller metric – Teichmueller geodesic – Thurston's asymmetric metric – extremal length – modulus – quasiconformal homeomorphism – measured foliation – ge"
 
  • hal-00129729, version 1
  • http://hal.archives-ouvertes.fr/hal-00129729
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  • Contributeur : Véronique Bertrand <>
  • Soumis le : Jeudi 8 Février 2007, 15:09:26
  • Dernière modification le : Jeudi 8 Février 2007, 17:07:28