{
  "id": "1503.06343",
  "version": "v1",
  "published": "2015-03-21T19:45:47.000Z",
  "updated": "2015-03-21T19:45:47.000Z",
  "title": "Asymptotic behavior of Cauchy hypersurfaces in constant curvature space-times",
  "authors": [
    "Mehdi Belraouti"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the asymptotic behavior of convex Cauchy hypersurfaces on maximal globally hyperbolic spatially compact space-times of constant curvature. We generalise the result of [11] to the (2+1) de Sitter and anti de Sitter cases. We prove that in these cases the level sets of quasi-concave times converge in the Gromov equivariant topology, when time goes to 0, to a real tree. Moreover, this limit does not depend on the choice of the time function. We also consider the problem of asymptotic behavior in the flat (n+1) dimensional case. We prove that the level sets of quasi-concave times converge in the Gromov equivariant topology, when time goes to 0, to a CAT (0) metric space. Moreover, this limit does not depend on the choice of the time function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-21T19:45:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic behavior",
      "constant curvature space-times",
      "cauchy hypersurfaces",
      "hyperbolic spatially compact space-times",
      "quasi-concave times converge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1355327
    }
  }
}