{
  "id": "math/0503023",
  "version": "v1",
  "published": "2005-03-01T20:17:28.000Z",
  "updated": "2005-03-01T20:17:28.000Z",
  "title": "Bounding dimension of ambient space by density for mean curvature flow",
  "authors": [
    "Maria Calle"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "For an ancient solution of the mean curvature flow, we show that each time slice M_t is contained in an affine subspace with dimension bounded in terms of the density and the dimension of the evolving submanifold. Recall that an ancient solution is a family M_t that evolves under mean curvature flow for all negative time t.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-01T20:17:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "mean curvature flow",
      "ambient space",
      "bounding dimension",
      "ancient solution",
      "time slice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3023C"
    }
  }
}