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 Events
Université de Montpellier, France
Fri 12 May 2017, 1:00pm
Diff. Geom, Math. Phys., PDE Seminar
Time and Location TBA
Prescribing the curvature of hyperbolic convex bodies
Time and Location TBA
Fri 12 May 2017, 1:00pm-2:00pm

Abstract

 The Gauss curvature of a convex body can be seen as a measure on the unit sphere (with some properties). For such a measure \mu , Alexandrov problem consists in proving the existence of a convex body whose curvature measure is \mu . In the Euclidean space, this problem is equivalent to an optimal transport problem on the sphere.
 
In this talk I will consider Alexandrov problem for convex bodies of the hyperbolic space. After defining the curvature measure, I will explain how to relate this problem to a non linear Kantorovich problem on the sphere and how to solve it.
 
Joint work with J\’er\^ome Bertrand.
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