{
  "id": "1302.0748",
  "version": "v1",
  "published": "2013-02-04T16:37:12.000Z",
  "updated": "2013-02-04T16:37:12.000Z",
  "title": "Homotopy of area decreasing maps by mean curvature flow",
  "authors": [
    "Andreas Savas-Halilaj",
    "Knut Smoczyk"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let $f:M\\to N$ be a smooth area decreasing map between two Riemannian manifolds $(M,\\gm)$ and $(N,\\gn)$. Under weak and natural assumptions on the curvatures of $(M,\\gm)$ and $(N,\\gn)$, we prove that the mean curvature flow provides a smooth homotopy of $f$ to a constant map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-04T16:37:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C42",
      "57R52",
      "35K55"
    ],
    "keywords": [
      "mean curvature flow",
      "smooth area decreasing map",
      "constant map",
      "riemannian manifolds",
      "natural assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.0748S"
    }
  }
}