Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
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 \(S^2\).
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