{
  "id": "2208.14280",
  "version": "v1",
  "published": "2022-08-30T13:59:39.000Z",
  "updated": "2022-08-30T13:59:39.000Z",
  "title": "A nonexistence result for rotating mean curvature flows in $\\mathbb{R}^{4}$",
  "authors": [
    "Wenkui Du",
    "Robert Haslhofer"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Some worrisome potential singularity models for the mean curvature flow are rotating ancient flows, i.e. ancient flows whose tangent flow at $-\\infty$ is a cylinder $\\mathbb{R}^k\\times S^{n-k}$ and that are rotating within the $\\mathbb{R}^k$-factor. We note that while the $\\mathbb{R}^k$-factor, i.e. the axis of the cylinder, is unique by the fundamental work of Colding-Minicozzi, the uniqueness of tangent flows by itself does not provide any information about rotations within the $\\mathbb{R}^k$-factor. In the present paper, we rule out rotating ancient flows among all ancient noncollapsed flows in $\\mathbb{R}^4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-30T13:59:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rotating mean curvature flows",
      "nonexistence result",
      "rotating ancient flows",
      "tangent flow",
      "worrisome potential singularity models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}