2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64711In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant mean curvature. This result can be seen as a generalization to higher dimensions of the well known Riemann mapping Theorem in the plane.Analysis of PDEsDifferential Geometry35J60; 53C21; 58G30A Riemannian mapping type Theorem in higher dimensions, Part I: the conformally flat case with umbilic boundarytext