{
  "id": "math/0307338",
  "version": "v1",
  "published": "2003-07-25T11:32:48.000Z",
  "updated": "2003-07-25T11:32:48.000Z",
  "title": "Constant mean curvature foliations of simplicial flat spacetimes",
  "authors": [
    "Lars Andersson"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Benedetti and Guadagnini have conjectured that the marked lenght spectrum of the constant mean curvature foliation $M_\\tau$ in a 2+1 dimensional flat spacetime $V$ with compact hyperbolic Cauchy surfaces converges, in the direction of the singularity, to that of the marked measure spectrum of the R-tree dual to the measured foliation corresponding to the translational part of the holonomy of $V$. We prove that this is the case for $n+1$ dimensional, $n \\geq 2$, {\\em simplicial} flat spacetimes with compact hyperbolic Cauchy surface. A simplicial spacetime is obtained from the Lorentz cone over a hyperbolic manifold by deformations corresponding to a simple measured foliation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-25T11:32:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant mean curvature foliation",
      "simplicial flat spacetimes",
      "compact hyperbolic cauchy surfaces converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7338A"
    }
  }
}