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

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.4335
 Bibcode:
 2007arXiv0711.4335N
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs;
 53C44
 EPrint:
 35 pages, submitted