{
  "id": "1005.4382",
  "version": "v1",
  "published": "2010-05-24T17:11:44.000Z",
  "updated": "2010-05-24T17:11:44.000Z",
  "title": "A Characterization of the Singular Time of the Mean Curvature Flow",
  "authors": [
    "Andrew A Cooper"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M^m_t\\hookrightarrow (N^{m+n}, h). We show that they are characterized by the blow-up of a trace A = H \\cdot II of the square of the second fundamental form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-24T17:11:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "mean curvature flow",
      "singular time",
      "characterization",
      "compact riemannian submanifolds",
      "second fundamental form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4382C"
    }
  }
}