The Aleksandrov problem and optimal transport on $S^n$

School of Mathematics Colloquium
Thursday, September 2, 2010 - 11:00am
1 hour (actually 50 minutes)
249 Skiles
Emory University
The purpose of this talk is to describe a variational approach to the problemof A.D. Aleksandrov concerning existence and uniqueness of a closed convexhypersurface in Euclidean space $R^{n+1}, ~n \geq 2$ with prescribed integral Gauss curvature. It is shown that this problem in variational formulation is closely connected with theproblem of optimal transport on $S^n$ with a geometrically motivated cost function.