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. 
Andr\'e Neves and Gang Tian