2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143096In 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.Optimization and ControlDifferential Geometrytext