{
  "annotation_id": "b09f79c5-95b8-42d4-a154-b3de7ba94f2e",
  "date_created": "2026-02-17T05:53:20.330000Z",
  "date_modified": "2026-02-17T05:53:20.330000Z",
  "file_hash": "8a84468f57a1e13b6de2ec8be0f36ee7363cb5557d4dd9eca2710219760fcc47",
  "private": false,
  "record": {
    "abstract": "We study compact non-selfsimilar ancient noncollapsed solutions to the mean curvature flow in $\\mathbb{R}^{n+1}$, called ancient ovals. Our main result is the classification of $k$-ovals: any $k$-oval (characterized by having cylindrical blow down $\\mathbb{R}^k\\times S^{n-k}$ and the quadratic bending asymptotics) belongs, up to space-time rigid motions and parabolic dilations, to the family of ancient ovals constructed by Haslhofer and the second author. Assuming the nonexistence of exotic ovals (recently proved by Bamler-Lai), this yields a classification of all ancient ovals and identifies the moduli space, modulo symmetries, with an open $(k-1)$-simplex modulo the symmetry of simplex. Although these conclusions are contained in the recent breakthrough of Bamler-Lai classifying all ancient asymptotically cylindrical flows and resolving the mean convex neighborhood conjecture, we give an alternative argument for the independently obtained classification of $k$-ovals in arbitrary dimensions based on a different spectral parametrization.",
    "arxiv_id": "2601.09441",
    "authors": [
      "Beomjun Choi",
      "Wenkui Du",
      "Ziyi Zhao"
    ],
    "categories": [
      "math.DG",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Classification of ancient ovals in higher dimensional mean curvature flow",
    "url": "https://arxiv.org/abs/2601.09441",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f38a3ba7-8019-4f87-8a7f-15b74c989d03",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}