{
  "id": "1401.3401",
  "version": "v3",
  "published": "2014-01-15T01:32:25.000Z",
  "updated": "2015-03-08T11:23:40.000Z",
  "title": "Mean curvature flow in submanifolds",
  "authors": [
    "Hiroshi Nakahara"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.DG"
  ],
  "abstract": "We obtain explicit solutions of the mean curvature flow in some submanifolds of the Euclidean space. We give particularly an explicit solution of the flow of a hypersurface in the Lagrangian self-expander $L$ which is constructed in the article of Joyce, Lee and Tsui and show that it converge to a minimal one.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-13T06:00:16.000Z",
      "abstract": "We obtain explicit solutions of the mean curvature flow in some submanifolds in the Euclidean space. We give particularly an explicit solution of the mean curvature flow of some hyperplane in the Lagrangian self-expander which is constructed by Joyce, Lee and Tsui and find therein a minimal hypersurface.",
      "comment": "6 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-03-08T11:23:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A07",
      "53A10",
      "53C42"
    ],
    "keywords": [
      "mean curvature flow",
      "submanifolds",
      "explicit solution",
      "lagrangian self-expander",
      "euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.3401N"
    }
  }
}