{
  "id": "1804.00018",
  "version": "v2",
  "published": "2018-03-30T18:11:49.000Z",
  "updated": "2019-01-14T20:55:52.000Z",
  "title": "Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions",
  "authors": [
    "S. Brendle",
    "K. Choi"
  ],
  "comment": "In this paper, we extend the result in arxiv:1711.00823 to higher dimensions, assuming uniform two-convexity",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we consider noncompact ancient solutions to the mean curvature flow in $\\mathbb{R}^{n+1}$ ($n \\geq 3$) which are strictly convex, uniformly two-convex, and noncollapsed. We prove that such an ancient solution is a rotationally symmetric translating soliton.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-01-14T20:55:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature flow",
      "convex ancient solutions",
      "higher dimensions",
      "uniqueness",
      "noncompact ancient solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}