{
  "id": "2003.08570",
  "version": "v1",
  "published": "2020-03-19T04:50:43.000Z",
  "updated": "2020-03-19T04:50:43.000Z",
  "title": "A class of curvature flows expanded by support function and curvature function",
  "authors": [
    "Shanwei Ding",
    "Guanghan Li"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we consider an expanding flow of closed, smooth, uniformly convex hypersurface in Euclidean \\mathbb{R}^{n+1} with speed u^\\alpha f^\\beta (\\alpha, \\beta\\in\\mathbb{R}^1), where u is support function of the hypersurface, f is a smooth, symmetric, homogenous of degree one, positive function of the principal curvature radii of the hypersurface. If \\alpha \\leq 0<\\beta\\leq 1-\\alpha, we prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalization, to a round sphere centered at the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-19T04:50:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "support function",
      "curvature function",
      "curvature flows",
      "principal curvature radii",
      "uniformly convex hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}