{
  "id": "0806.1758",
  "version": "v2",
  "published": "2008-06-10T21:41:11.000Z",
  "updated": "2008-09-03T18:12:22.000Z",
  "title": "The harmonic mean curvature flow of nonconvex surfaces in $\\mathbb{R}^3$",
  "authors": [
    "Panagiota Daskalopoulos",
    "Natasa Sesum"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We consider a compact, star-shaped, mean convex hypersurface $\\Sigma^2\\subset \\mathbb{R}^3$. We prove that in some cases the flow exists until it shrinks to a point in a spherical manner, which is very typical for convex surfaces as well (see \\cite{An1}). We also prove that in the case we have a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time $T < \\infty$ at which the flow shrinks to a point asymptotically spherically.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-03T18:12:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "harmonic mean curvature flow",
      "nonconvex surfaces",
      "mean convex hypersurface",
      "finite time",
      "smooth solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1758D"
    }
  }
}