Resumen de The Monge problem for supercritical Mañé potentials on compact manifolds

Patrick Bernard, Boris Buffoni

• We prove the existence of optimal transport maps for the Monge problem when the cost is a Finsler distance on a compact manifold. Our point of view consists in considering the distance as a Mañé potential, and to rely on recent developments in the theory of viscosity solutions of the Hamilton¿Jacobi equation.