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Filippo Mazzoli

Constant Gaussian curvature surfaces in hyperbolic 3-manifolds
Thursday, 12 December, 2019 - 12:45
Résumé : 

By a result of Labourie, every 3-dimensional hyperbolic end admits a unique foliation by constant Gaussian curvature surfaces (briefly CGC-surfaces). In 1992, the same author described two families of parametrizations of the space of hyperbolic ends E(S) (with S closed surface of genus greater than 1), using the geometric data of the leaves of the foliation by CGC-surfaces.

In this talk, I will show how the recent results of Belraouti and Quinn allow us to recover the “classical” Thurston’s and Schwarzian parametrizations of E(S) from the asymptotic of Labourie’s parametrizations. In addition, I will describe a series of interesting consequences of this phenomenon, such as a new characterization of the notion of renormalized volume in terms of the CGC-foliation, and a generalization of McMullen's Kleinian reciprocity theorem.

Institution de l'orateur : 
Université du Luxembourg
Thème de recherche : 
Théorie spectrale et géométrie
Salle : 
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