{
  "id": "1004.2938",
  "version": "v1",
  "published": "2010-04-17T02:59:59.000Z",
  "updated": "2010-04-17T02:59:59.000Z",
  "title": "Improved breakdown criterion for Einstein vacuum equations in CMC gauge",
  "authors": [
    "Qian Wang"
  ],
  "categories": [
    "math.AP",
    "gr-qc",
    "math.DG"
  ],
  "abstract": "Let $\\M_*=\\cup_{t\\in [t_0, t_*)} \\Sigma_t$ be a part of vacuum globally hyperbolic space-time $(\\bM, \\bg)$, foliated by constant mean curvature hypersurfaces $\\Sigma_t$ with $t_0<t_*<0$. We show that the foliation can be extended beyond $t_*$ if the second fundamental form $k$ and the lapse function $n$ satisfy $$ \\int_{t_0}^{t_*}(\\|k\\|_{L^\\infty(\\Sigma_t)}+\\|\\nab \\log n\\|_{L^\\infty(\\Sigma_t)}) dt <\\infty. $$ This improves the existing breakdown criteria for Einstein vacuum equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-17T02:59:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "einstein vacuum equations",
      "breakdown criterion",
      "cmc gauge",
      "constant mean curvature hypersurfaces",
      "second fundamental form"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1002/cpa.20388"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 852477,
      "adsabs": "2010arXiv1004.2938W"
    }
  }
}