2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118106We prove existence and uniqueness of foliations by stable spheres with constant mean curvature for 3-manifolds which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass. These metrics arise naturally as spacelike timeslices for solutions of the Einstein equation with a negative cosmological constant.39 pages, submitted. Decay conditions on Lemma 6.3 and Theorem 1.3 correctedDifferential GeometryMathematical Physics53A10text