{
  "id": "1904.07835",
  "version": "v1",
  "published": "2019-04-16T17:27:19.000Z",
  "updated": "2019-04-16T17:27:19.000Z",
  "title": "Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case",
  "authors": [
    "S. Brendle"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In [4], we proved that every noncompact ancient $\\kappa$-solution to the Ricci flow in dimension $3$ is either locally isometric to a family of shrinking cylinders, or isometric to the Bryant soliton. In the same paper, we announced that the same method implies that compact ancient $\\kappa$-solutions are rotationally symmetric. In this note we provide the details of this argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-16T17:27:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci flow",
      "compact case",
      "ancient solutions",
      "rotational symmetry",
      "noncompact ancient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}