Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
type: Item
instance of: scholarly article
title: Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
zbMATH Open document ID: 1195.53096
author: André Neves
published in: Journal of Differential Geometry
publication date: 2010-06-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/0711.4335
full work available at URL: v84n1
review text: The author constructs a solution to the inverse mean curvature flow on an asympotically hyperbolic \(3\)-manifold that does not have the convergence properties needed in order to prove a Penrose-type inequality. This result is in sharp contrast with the asymptotically flat case in which the Penrose inequality is valid. The main idea of proof uses results by Y. Shi and L. F. Tam on the boundary behaviour of compact manifolds and inverse mean curvature flow. By assuming the manifolds the author constructs satisfies the Penrose inequality the author proves a nontrivial inequality for functions on \(S^2\).
reviewed by: Shu-Yu Hsu
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 5724753
zbMATH Keywords: inverse mean curvature flow
zbMATH Keywords: asympotically hyperbolic \(3\)-manifold
zbMATH Keywords: convergence properties
zbMATH Keywords: Penrose-type inequality
Wikidata QID: Q115171373
MaRDI profile type: Publication
OpenAlex ID: W1486701209
arXiv ID: 0711.4335
DOI: 10.4310/JDG/1271271798
description: scientific article