Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds

Andre Neves

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arXiv · 0711.4335

Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds

Andre Neves

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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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Andre Neves. 2007-11-27. Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds. https://arxiv.org/abs/0711.4335

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