{
  "id": "1111.4616",
  "version": "v1",
  "published": "2011-11-20T07:51:53.000Z",
  "updated": "2011-11-20T07:51:53.000Z",
  "title": "Surfaces moving by powers of Gauss curvature",
  "authors": [
    "Ben Andrews",
    "Xuzhong Chen"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove that strictly convex surfaces moving by $K^{\\alpha/2}$ become spherical as they contract to points, provided $\\alpha$ lies in the range $[1,2]$. In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution of curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-20T07:51:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35K96",
      "58J35"
    ],
    "keywords": [
      "gauss curvature",
      "reaction terms",
      "natural candidate",
      "curvature pinching quantity",
      "arbitrary functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4616A"
    }
  }
}