2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128310The purpose of this paper is to show that in a finite dimensional metric space with Alexandrov's curvature bounded below, Monge's transport problem for the quadratic cost admits a unique solution.Differential GeometryAnalysis of PDEsExistence and uniqueness of optimal maps on Alexandrov spacestext