{
  "id": "2009.12273",
  "version": "v1",
  "published": "2020-09-25T14:42:42.000Z",
  "updated": "2020-09-25T14:42:42.000Z",
  "title": "A Reverse Isoperimetric Inequality and its Application to the Gradient Flow of the Helfrich Functional",
  "authors": [
    "Simon Blatt"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We prove a quantitative reverse isoperimetric inequality for embedded surfaces with Willmore energy bounded away from $8\\pi$. We use this result to analyze the negative $L^2$ gradient flow of the Willmore energy plus a positive multiple of the inclosed volume. We show that initial surfaces of Willmore energy less than $8\\pi$ with positive inclosed volume converge to a round point in finite or infinite time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-25T14:42:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47J35",
      "53A05"
    ],
    "keywords": [
      "gradient flow",
      "helfrich functional",
      "application",
      "willmore energy plus",
      "inclosed volume"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}