{
  "id": "1708.04827",
  "version": "v1",
  "published": "2017-08-16T09:52:04.000Z",
  "updated": "2017-08-16T09:52:04.000Z",
  "title": "Evolution of Locally Convex Closed Curves in Nonlocal Curvature Flows",
  "authors": [
    "Natasa Sesum",
    "Dong-Ho Tsai",
    "Xiao-Liu Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge to an $m$-fold circle as time goes to infinity. For the area-preserving flow, the positivity of the enclosed algebraic area determines whether the curvature blows up in finite time or not, while for the length-preserving flow, it is the positivity of an energy associated with initial curve that plays such a role.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-16T09:52:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "locally convex closed curves",
      "nonlocal curvature flows",
      "initial curve",
      "finite time",
      "enclosed algebraic area determines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}