Christopher R. Nerz: Foliations of asymptotically flat manifolds and their evolution in time

For the study of asymptotically flat manifolds in mathematical general relativity, surfaces of constant mean curvature (CMC) have proved to be a useful tool. In 1996, Huisken-Yau showed that any asymptotically flat Riemannian manifold can be uniquely foliated by closed CMC surfaces. Furthermore, they interpreted this foliation as a definition of the center of mass. We present a new existence result for this foliation and prove that this definition is compatible with the definition of linear momentum by Arnowitt-Deser-Misner: The evolution of this foliation (asymptotically) corresponds to a translation with direction given by the quotient of (ADM) linear momentum and mass - equivalent to the center of mass in Newtonian systems.