On the capacity of surfaces in asymptotically flat half-space

Abstract

The purpose of this work is to establish an upper bound for the capacity of the surface in a three-dimensional asymptotically flat half-space with nonnegative scalar curvature and mean convex boundary. If the equality holds, we show a rigidity result involving the half-Schwarzschild space. In order to prove our result we use the inverse of mean curvature flow for hypersurfaces with boundary.