Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds

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dc.creatorNeves, Andre
dc.date2007-11-27
dc.date.accessioned2026-07-07T08:45:26Z
dc.date.available2026-07-07T08:45:26Z
dc.descriptionWe 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 $S^2$.
dc.description35 pages, submitted
dc.identifierhttps://arxiv.org/abs/0711.4335
dc.identifierhttp://arxiv.org/abs/0711.4335
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142965
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C44
dc.titleInsufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
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