{
  "id": "1703.10711",
  "version": "v1",
  "published": "2017-03-30T23:32:11.000Z",
  "updated": "2017-03-30T23:32:11.000Z",
  "title": "Curve diffusion and straightening flows on parallel lines",
  "authors": [
    "Glen Wheeler",
    "Valentina-Mira Wheeler"
  ],
  "comment": "35 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study families of immersed curves $\\gamma:(-1,1)\\times[0,T)\\rightarrow\\mathbb{R}^2$ with free boundary supported on parallel lines $\\{\\eta_1, \\eta_2\\}:\\mathbb{R}\\rightarrow\\mathbb{R}^2$ evolving by the curve diffusion flow and the curve straightening flow. The evolving curves are orthogonal to the boundary and satisfy a no-flux condition. We give estimates and monotonicity on the normalised oscillation of curvature, yielding global results for the flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T23:32:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "parallel lines",
      "curve diffusion flow",
      "no-flux condition",
      "curve straightening flow",
      "free boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}