Existence and Uniqueness of Constant Mean Curvature Foliation of Asymptotically Hyperbolic 3-Manifolds

We 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.