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arXiv · 1709.06550

On a Minkowski-like inequality for asymptotically flat static manifolds

Stephen McCormick
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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.

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Stephen McCormick. 2017-09-19. On a Minkowski-like inequality for asymptotically flat static manifolds. https://doi.org/10.1090/proc/14047

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