Seminars & Colloquia Calendar
Closed convex hypersurfaces with prescribed integral Gauss curvature and optimal transport on a sphere
Vladimir Oliker, Emory University
Location: Hill 705
Date & time: Tuesday, 02 April 2019 at 1:40PM - 3:00PM
Abstract: In his book on Convex Polyhedra (1950) A.D. Aleksandrov raised a general question of finding variational statements and proofs of existence of polytopes with given geometric data. The first goal of this talk is to describe a variational solution to the problem of existence of a closed convex hypersurface in Euclidean space with prescribed integral Gauss curvature. Our solution includes the case of a convex polytope. This
problem ("Aleksandrov's problem") was first posed and solved in 1939 by Aleksandrov himself. He used a non-variational approach.
The second goal of the talk is to show that in variational form the Aleksandrov problem is closely connected with the theory of optimal mass transport of Monge-Kantorovich.