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.References
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