BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Abderrahim Mesbah: "The induced metric and bending lamination  on 
 the boundary of convex hyperbolic 3-manifolds."
DTSTART:20231115T130000Z
DTEND:20231115T140000Z
DTSTAMP:20260522T124500Z
UID:indico-event-10750@indico.math.cnrs.fr
DESCRIPTION:Let S be a closed hyperbolic surface and let M = S×(0\,1). Su
 ppose 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.\n
 \nhttps://indico.math.cnrs.fr/event/10750/
LOCATION:435 (UMPA)
URL:https://indico.math.cnrs.fr/event/10750/
END:VEVENT
END:VCALENDAR