{
  "id": "1610.08933",
  "version": "v1",
  "published": "2016-10-27T19:05:13.000Z",
  "updated": "2016-10-27T19:05:13.000Z",
  "title": "Asymptotic behavior of flows by powers of the Gaussian curvature",
  "authors": [
    "Simon Brendle",
    "Kyeongsu Choi",
    "Panagiota Daskalopoulos"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We consider a one-parameter family of strictly convex hypersurfaces in $\\mathbb{R}^{n+1}$ moving with speed $- K^\\alpha \\nu$, where $\\nu$ denotes the outward-pointing unit normal vector and $\\alpha \\geq \\frac{1}{n+2}$. For $\\alpha > \\frac{1}{n+2}$, we show that the flow converges to a round sphere after rescaling. In the affine invariant case $\\alpha=\\frac{1}{n+2}$, our arguments give an alternative proof of the fact that the flow converges to an ellipsoid after rescaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-27T19:05:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian curvature",
      "asymptotic behavior",
      "flow converges",
      "outward-pointing unit normal vector",
      "affine invariant case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}