On Large Volume Preserving Stable CMC Surfaces in Initial Data Sets
On Large Volume Preserving Stable CMC Surfaces in Initial Data Sets
Let $(M, g)$ be a complete 3-dimensional asymptotically flat manifold with everywhere positive scalar curvature. We prove that, given a compact subset $K \subset M$, all volume preserving stable constant mean curvature surfaces of sufficiently large area will avoid $K$. This complements the results of G. Huisken and S.-T. Yau …