2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145419In this paper we prove that under a lower bound on the Ricci curvature and an asymptotic assumption on the scalar curvature, a complete conformally compact manifold $(M^{n+1},g)$, with a pole $p$ and with the conformal infinity in the conformal class of the round sphere, has to be the hyperbolic space.23 pagesDifferential Geometrytext