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UID:4999@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20231214T110000
DTEND;TZID=Europe/Paris:20231214T120000
DTSTAMP:20240524T072506Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-45-2/
SUMMARY: (...): On the boundary of convex hyperbolic manifolds.
DESCRIPTION:: Let S be a closed hyperbolic surface and let M = S×(0\,1). S
 uppose h is a Riemannian metric on S with curvature strictly greater than 
 −1\, h∗ is a Riemannian metric on S with curvature strictly less than 
 1\, and every contractible closed geodesic with respect to h∗ has length
  strictly greater than 2π. Let L be a measured lamination on S such that 
 every closed leaf has weight strictly less than π. Then\, we prove the ex
 istence of a convex hyperbolic metric g on the interior of M that induces 
 the Riemannian metric h (respectively h∗) as the first (respectively thi
 rd) fundamental form on S×{0} and induces a pleated surface structure on 
 S×{1} with bending lamination L. This statement remains valid even in lim
 iting cases where the curvature of h is constant and equal to −1. Additi
 onally\, when considering a conformal class c on S\, we show that there ex
 ists a convex hyperbolic metric g on the interior of M that induces c on S
 ×{0}\, which is viewed as one component of the ideal boundary at infinity
  of (M\,g)\, and induces a pleated surface structure on S×{1} with bendin
 g lamination L. Our proof differs from previous work by Lecuire for these 
 two last cases. Moreover\, when we consider a lamination which is small en
 ough\, in a sense that we will define\, and a hyperbolic metric\, we show 
 that the metric on the interior of M that realizes these data is unique.
CATEGORIES:Séminaire,Géométrie et Topologie de Marseille
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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DTSTART:20231029T020000
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