Statut  Confirmé 
Série  MATHIHES 
Domaines  hepth 
Date  Lundi 16 Octobre 2017 
Heure  14:30 
Institut  IHES 
Salle  Amphithéâtre Léon Motchane 
Nom de l'orateur  Schlenker 
Prenom de l'orateur  JeanMarc 
Addresse email de l'orateur  
Institution de l'orateur  Université du Luxembourg 
Titre  The renormalized volume of quasifuchsian manifolds 
Résumé  Quasifuchsian manifolds are an important class of hyperbolic 3manifolds, classically parametrized by two copies of Teichmüller space. Their volume is infinite, but they have a welldefined finite "renormalized volume" which has nice properties, both analytic and "coarse". In particular, considered as a function over Teichmüller space, the renormalized volume provides a Kähler potential for the WeilPetersson metric; moreover, it is within bounded additive constants of the volume of the convex core and is bounded from above by the WeilPetersson distance between the conformal structures at infinity. After describing these properties, we will outline some recent applications (by Kojima, McShane, Brock, Bromberg, Bridgeman, and others) to the WeilPetersson geometry of Teichmüller space or the geometry of hyperbolic 3manifolds that fiber over the circle. We will then explain how properties of the renormalized volume suggest new questions and viewpoints on quasifuchsian manifolds. The talk will be accessible to nonexperts. 
Numéro de preprint arXiv  
Commentaires  Séminaire Géométrie et groupes discrets 
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