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On a Minkowski-like inequality for asymptotically flat static manifolds


Author: Stephen McCormick
Journal: Proc. Amer. Math. Soc. 146 (2018), 4039-4046
MSC (2010): Primary 53C20; Secondary 83C99, 53C44
DOI: https://doi.org/10.1090/proc/14047
Published electronically: April 17, 2018
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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 $ \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
Email: stephen.mccormick@math.uu.se

DOI: https://doi.org/10.1090/proc/14047
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
Article copyright: © Copyright 2018 American Mathematical Society

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