Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142965We 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 $S^2$.35 pages, submittedDifferential GeometryAnalysis of PDEs53C44Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifoldstext