%0 Journal Article
%T Rectifiability of Optimal Transportation Plans
%A Robert J. McCann
%A Brendan Pass
%A Micah Warren
%J Mathematics
%D 2010
%I arXiv
%X The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere.
%U http://arxiv.org/abs/1003.4556v1