{
  "id": "0902.2261",
  "version": "v2",
  "published": "2009-02-13T05:25:11.000Z",
  "updated": "2009-03-20T00:42:48.000Z",
  "title": "Singularity Profile in the Mean Curvature Flow",
  "authors": [
    "Weimin Sheng",
    "Xu-Jia Wang"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we study the geometry of first time singularities of the mean curvature flow. By the curvature pinching estimate of Huisken and Sinestrari, we prove that a mean curvature flow of hypersurfaces in the Euclidean space $\\R^{n+1}$ with positive mean curvature is $\\kappa$-noncollapsing, and a blow-up sequence converges locally smoothly along a subsequence to a smooth, convex blow-up solution. As a consequence we obtain a local Harnack inequality for the mean convex flow.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-20T00:42:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35K55"
    ],
    "keywords": [
      "mean curvature flow",
      "singularity profile",
      "sequence converges",
      "convex blow-up solution",
      "first time singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2261S"
    }
  }
}