Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
By A. Neves. 2007
71 citations recorded by the source corpus.
We 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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3bc1841b268ca6f3ee7844b1ad6e2ac973849383
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- The Penrose Inequality for Asymptotically Locally Hyperbolic Spaces with Nonpositive Mass (2013, background): “The di↵erence between our result here and the one in [19] can be traced to the fact that if the mass aspect is positive, then a desired inequality goes in the wrong direction, whereas for nonpositive mass aspect, it goes in the right direction.”
- Present status of the Penrose inequality (2009, background): “However, a recent result by Neves [130] shows that this is not possible in general.”