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

Abstract

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.