The foliation of asymptotically hyperbolic manifolds by surfaces of constant mean curvature (including the evolution equations and estimates)

The Hamiltonian formulation of the Einstein equations is achieved by means of a foliation of the background Lorentz Manifold. The usage of maximal surfaces is the frequently applied gauge for numerical research of asymptotically flat manifolds. In this paper we construct a foliation of asymptotically hyperbolic 3-surfaces through 2-surfaces (with constant mean curvature) homeomorphic to spheres. This is established by using the volume preserving mean curvature flow. These spheres define a geometric intrinsic radius coordinate near infinity and therefore define a center of mass for the Bondi case.