English

On a Minkowski-like inequality for asymptotically flat static manifolds

Differential Geometry 2018-06-28 v4 General Relativity and Quantum Cosmology

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.

Keywords

Cite

@article{arxiv.1709.06550,
  title  = {On a Minkowski-like inequality for asymptotically flat static manifolds},
  author = {Stephen McCormick},
  journal= {arXiv preprint arXiv:1709.06550},
  year   = {2018}
}

Comments

10 pages. Proc. Amer. Math. Soc. V4: Fixed typo in eq (1.1)

R2 v1 2026-06-22T21:48:32.537Z