Thomas Körber - Foliations of asymptotically flat 3-manifolds by stable constant mean curvature spheres

Stable constant mean curvature spheres encode important information on the asymptotic geometry of initial data sets for isolated gravitational systems. In this talk, I will present a short new proof (joint with M. Eichmair) based on Lyapunov-Schmidt reduction of the existence of an asymptotic foliation of such an initial data set by stable constant mean curvature spheres. In the case where the scalar curvature is non-negative, our method also shows that the leaves of this foliation are the only large stable constant mean curvature spheres that enclose the center of the initial data set.