{
  "id": "1204.6116",
  "version": "v1",
  "published": "2012-04-27T06:37:13.000Z",
  "updated": "2012-04-27T06:37:13.000Z",
  "title": "The Stability of Self-Shrinkers of Mean Curvature Flow in Higher Codimension",
  "authors": [
    "Yng-Ing Lee",
    "Yang-Kai Lue"
  ],
  "comment": "We in the end of 2010, obtained the same foundation part of the article arXiv:1204.5010v1 by B. Andrews, H. Li and Y. Wei, entitled with \"F-stability for self-shrinking solutions to mean curvature flow\". In our article, we at the same time showed the unstability of Anciaux's closed Lagrangian self-shrinkers",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we generalize Colding and Minicozzi's work \\cite{CM} on the stability of self-shrinkers in the hypersurface case to higher co-dimensional cases. The first and second variation formulae of the $F$-functional are derived and an equivalent condition to the stability in general codimension is found. Moreover, we show that the closed Lagrangian self-shrinkers given by Anciaux in \\cite{An} are unstable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-27T06:37:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature flow",
      "higher codimension",
      "higher co-dimensional cases",
      "second variation formulae",
      "minicozzis work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.6116L"
    }
  }
}