{
  "id": "1304.0926",
  "version": "v2",
  "published": "2013-04-03T11:51:51.000Z",
  "updated": "2014-04-13T23:14:37.000Z",
  "title": "Mean curvature flow of mean convex hypersurfaces",
  "authors": [
    "Robert Haslhofer",
    "Bruce Kleiner"
  ],
  "comment": "Minor changes to facilitate applications to mean curvature flow with surgery",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In the last 15 years, White and Huisken-Sinestrari developed a far-reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise description of singularities and of high curvature regions in a mean convex flow. In the present paper, we give a new treatment of the theory of mean convex (and k-convex) flows. This includes: (1) an estimate for derivatives of curvatures, (2) a convexity estimate, (3) a cylindrical estimate, (4) a global convergence theorem, (5) a structure theorem for ancient solutions, and (6) a partial regularity theorem. Our new proofs are both more elementary and substantially shorter than the original arguments. Our estimates are local and universal. A key ingredient in our new approach is the new non- collapsing result of Andrews. Some parts are also inspired by the work of Perelman. In a forthcoming paper, we will give a new construction of mean curvature flow with surgery based on the theorems established in the present paper.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-13T23:14:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35K55"
    ],
    "keywords": [
      "mean curvature flow",
      "mean convex hypersurfaces",
      "partial regularity theorem",
      "global convergence theorem",
      "mean convex flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0926H"
    }
  }
}