{
  "id": "math/0507325",
  "version": "v1",
  "published": "2005-07-15T22:55:26.000Z",
  "updated": "2005-07-15T22:55:26.000Z",
  "title": "Self-shrinkers of the mean curvature flow in arbitrary codimension",
  "authors": [
    "Knut Smoczyk"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.DG"
  ],
  "abstract": "For hypersurfaces of dimension greater than one, Huisken showed that compact self-shrinkers of the mean curvature flow with positive scalar mean curvature are spheres. We will prove the following extension: A compact self-similar solution in arbitrary codimension and of dimension greater than one is spherical, i.e. contained in a sphere, if and only if the mean curvature vector \\be H\\ee is non-vanishing and the principal normal \\be\\nu\\ee is parallel in the normal bundle. We also give a classification of complete noncompact self-shrinkers of that type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-15T22:55:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "mean curvature flow",
      "arbitrary codimension",
      "dimension greater",
      "mean curvature vector",
      "compact self-similar solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7325S"
    }
  }
}