{
  "id": "1104.0971",
  "version": "v1",
  "published": "2011-04-05T22:58:43.000Z",
  "updated": "2011-04-05T22:58:43.000Z",
  "title": "The extension and convergence of mean curvature flow in higher codimension",
  "authors": [
    "Kefeng Liu",
    "Hongwei Xu",
    "Fei Ye",
    "Entao Zhao"
  ],
  "comment": "29 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension $d\\geq1$, which generalizes the extension theorem for the mean curvature flow of hypersurfaces due to Le-\\v{S}e\\v{s}um \\cite{LS} and the authors \\cite{XYZ1,XYZ2}. Using the extension theorem, we prove two convergence theorems for the mean curvature flow of closed submanifolds in ${R}^{n+d}$ under suitable integral curvature conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-05T22:58:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature flow",
      "higher codimension",
      "extension theorem",
      "suitable integral curvature conditions",
      "submanifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0971L"
    }
  }
}