{
  "id": "0711.4335",
  "version": "v1",
  "published": "2007-11-27T19:46:55.000Z",
  "updated": "2007-11-27T19:46:55.000Z",
  "title": "Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds",
  "authors": [
    "Andre Neves"
  ],
  "comment": "35 pages, submitted",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "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 $S^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-27T19:46:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "asymptotically hyperbolic manifolds",
      "insufficient convergence",
      "combining inverse mean curvature flow",
      "main idea consists",
      "shi-tam regarding boundary behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.4335N"
    }
  }
}