{
  "id": "2001.00341",
  "version": "v1",
  "published": "2020-01-02T06:44:27.000Z",
  "updated": "2020-01-02T06:44:27.000Z",
  "title": "Uniform Lipschitz continuity of the isoperimetric profile of compact surfaces under normalized Ricci flow",
  "authors": [
    "Yizhong Zheng"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that the isoperimetric profile $h_{g(t)}(\\xi)$ of a compact Riemannian manifold $(M,g)$ is jointly continuous when metrics $g(t)$ vary continuously. We also show that, when $M$ is a compact surface and $g(t)$ evolves under normalized Ricci flow, $h^2_{g(t)}(\\xi)$ is uniform Lipschitz continuous and hence $h_{g(t)}(\\xi)$ is uniform locally Lipschitz continuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-02T06:44:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normalized ricci flow",
      "uniform lipschitz continuity",
      "compact surface",
      "isoperimetric profile",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}