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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a Minkowski-like inequality for asymptotically flat static manifolds
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by Stephen McCormick PDF
Proc. Amer. Math. Soc. 146 (2018), 4039-4046 Request permission

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.
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Additional Information
  • Stephen McCormick
  • Affiliation: Institutionen för Matematik, Kungliga Tekniska högskolan, 100 44 Stockholm, Sweden
  • Address at time of publication: Matematiska institutionen, Uppsala universitet, 751 06 Uppsala, Sweden
  • MR Author ID: 1085293
  • ORCID: 0000-0001-9536-9908
  • Email: stephen.mccormick@math.uu.se
  • Received by editor(s): November 24, 2017
  • Received by editor(s) in revised form: December 6, 2017
  • Published electronically: April 17, 2018
  • Communicated by: Guofang Wei
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 4039-4046
  • MSC (2010): Primary 53C20; Secondary 83C99, 53C44
  • DOI: https://doi.org/10.1090/proc/14047
  • MathSciNet review: 3825857