{
  "id": "1811.02559",
  "version": "v1",
  "published": "2018-11-06T18:59:38.000Z",
  "updated": "2018-11-06T18:59:38.000Z",
  "title": "Ancient solutions to the Ricci flow in dimension 3",
  "authors": [
    "S. Brendle"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient $\\kappa$-solution. We prove that the every noncompact ancient $\\kappa$-solution in dimension $3$ is isometric to either the shrinking cylinders (or a quotient thereof), or the Bryant soliton.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-06T18:59:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci flow",
      "ancient solutions",
      "finite-time singularity",
      "bryant soliton",
      "noncompact ancient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}