{
  "id": "1611.07597",
  "version": "v1",
  "published": "2016-11-23T01:36:22.000Z",
  "updated": "2016-11-23T01:36:22.000Z",
  "title": "Self-similar solutions of $σ_k^α$-curvature flow",
  "authors": [
    "Shanze Gao",
    "Hui Ma"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper, employing a new inequality, we show that under certain curvature pinching condition, the strictly convex closed smooth self-similar solution of $\\sigma_k^{\\alpha}$-flow must be a round sphere. We also obtain a similar result for the solutions of $F=-\\langle X, e_{n+1}\\rangle \\, (*)$ with a non-homogeneous function $F$. At last, we prove that if $F$ can be compared with $\\frac{(n-k+1)\\sigma_{k-1}}{k\\sigma_{k}}$, then a closed strictly $k$-convex solution of $(*)$ must be a round sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-23T01:36:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C40"
    ],
    "keywords": [
      "curvature flow",
      "convex closed smooth self-similar solution",
      "round sphere",
      "strictly convex closed smooth self-similar",
      "curvature pinching condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}