{
  "id": "1106.4583",
  "version": "v3",
  "published": "2011-06-22T21:20:08.000Z",
  "updated": "2012-12-14T00:47:30.000Z",
  "title": "Helicoidal surfaces rotating/translating under the mean curvature flow",
  "authors": [
    "Hoeskuldur P. Halldorsson"
  ],
  "comment": "21 pages, 22 figures, final version",
  "doi": "10.1007/s10711-012-9716-2",
  "categories": [
    "math.DG"
  ],
  "abstract": "We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-14T00:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53A10",
      "53C42"
    ],
    "keywords": [
      "mean curvature flow",
      "helicoidal surfaces rotating/translating",
      "constant mean curvature helicoidal surfaces",
      "limiting behaviour",
      "classical helicoidal minimal surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4583H"
    }
  }
}