On a Minkowski-like inequality for asymptotically flat static manifolds

Abstract:

The Minkowski inequality is a classical inequality in differential geometry giving a bound from below on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving versions of this inequality for manifolds other than $\mathbb {R}^n$; for example, such an inequality holds for surfaces in spatial Schwarzschild and AdS-Schwarzschild manifolds. In this note, we adapt a recent analysis of Y. Wei to prove a Minkowski-like inequality for general static asymptotically flat manifolds.