Brendle’s Inequality on Static Manifolds

Xiaodong Wang, Ye Kai Wang

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

We generalize Brendle’s geometric inequality considered in Brendle (Publ Math Inst Hautes Études Sci 117:247–269, 2013) to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a consequence, we obtain a reverse Penrose inequality on static asymptotically locally hyperbolic manifolds in the spirit of Chruściel and Simon (J Math Phys 42(4):1779–1817, 2001).

Original languageEnglish
Pages (from-to)152-169
Number of pages18
JournalJournal of Geometric Analysis
Volume28
Issue number1
DOIs
Publication statusPublished - 2018 Jan 1

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Geometric Inequalities
Hyperbolic Manifold
Mean Curvature
Hypersurface
Reverse
Horizon
Generalise

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Wang, Xiaodong ; Wang, Ye Kai. / Brendle’s Inequality on Static Manifolds. In: Journal of Geometric Analysis. 2018 ; Vol. 28, No. 1. pp. 152-169.
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Wang, X & Wang, YK 2018, 'Brendle’s Inequality on Static Manifolds', Journal of Geometric Analysis, vol. 28, no. 1, pp. 152-169. https://doi.org/10.1007/s12220-017-9814-3

Brendle’s Inequality on Static Manifolds. / Wang, Xiaodong; Wang, Ye Kai.

In: Journal of Geometric Analysis, Vol. 28, No. 1, 01.01.2018, p. 152-169.

Research output: Contribution to journal › Article

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AU - Wang, Ye Kai

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AB - We generalize Brendle’s geometric inequality considered in Brendle (Publ Math Inst Hautes Études Sci 117:247–269, 2013) to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a consequence, we obtain a reverse Penrose inequality on static asymptotically locally hyperbolic manifolds in the spirit of Chruściel and Simon (J Math Phys 42(4):1779–1817, 2001).

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Wang X, Wang YK. Brendle’s Inequality on Static Manifolds. Journal of Geometric Analysis. 2018 Jan 1;28(1):152-169. https://doi.org/10.1007/s12220-017-9814-3

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