Calculus of Variations and Geometric Measure Theory

A. Figalli

The Monge problem on non-compact manifolds

created by figalli on 31 May 2006


Accepted Paper

Inserted: 31 may 2006

Journal: Rend. Sem. Mat. Univ. Padova
Year: 2006


In this paper we prove the existence of an optimal transport map on non-compact manifolds for a large class of cost functions that includes the case $c(x,y)=d(x,y)$, under the only hypothesis that the source measure is absolutely continuous with respect to the volume measure. In particular, we assume compactness neither of the support of the source measure nor of that of the target measure.

Keywords: optimal transportation, ma\ né potential, distance-like costs