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January 2010 Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
André Neves
J. Differential Geom. 84(1): 191-229 (January 2010). DOI: 10.4310/jdg/1271271798

Abstract

We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose–type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow with work done by Shi–Tam regarding boundary behavior of compact manifolds. Assuming the Penrose inequality holds, we also derive a nontrivial inequality for functions on $S^2$.

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André Neves. "Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds." J. Differential Geom. 84 (1) 191 - 229, January 2010. https://doi.org/10.4310/jdg/1271271798

Information

Published: January 2010
First available in Project Euclid: 14 April 2010

zbMATH: 1195.53096
MathSciNet: MR2629514
Digital Object Identifier: 10.4310/jdg/1271271798

Rights: Copyright © 2010 Lehigh University

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Vol.84 • No. 1 • January 2010
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