Calculus of Variations and Geometric Measure Theory

A. Fathi - A. Figalli

Optimal transportation on non-compact manifolds

created by figalli on 07 Nov 2007


Accepted Paper

Inserted: 7 nov 2007

Journal: Israel J. Math.
Year: 2007


In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type $d^r,r>1$, where $d$ is the Riemannian distance of a complete Riemannian manifold, hold without any curvature restriction.