On a Minkowski-like inequality for asymptotically flat static manifolds

TL;DR

This paper extends the Minkowski inequality to a broad class of static asymptotically flat manifolds, generalizing classical geometric bounds from Euclidean space to more complex geometric settings.

Contribution

It adapts recent analytical techniques to establish a Minkowski-like inequality for static asymptotically flat manifolds, broadening the scope of geometric inequalities.

Findings

Proves a Minkowski-like inequality for static asymptotically flat manifolds.

Generalizes known inequalities from Euclidean and Schwarzschild spaces.

Uses analysis inspired by Y. Wei's recent work.

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 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.