## Prescribing the curvature of hyperbolic convex bodies: Philippe Castillon

- Date: 05/12/2017
- Time: 13:00

University of British Columbia

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 Jerome Bertrand.

Location: ESB 4127 (PIMS videoconferencing room)

Fri 12 May 2017, 1:00pm-2:00pm