{
  "id": "1202.1264",
  "version": "v3",
  "published": "2012-02-06T20:26:49.000Z",
  "updated": "2013-02-03T21:27:03.000Z",
  "title": "Rotational symmetry of self-similar solutions to the Ricci flow",
  "authors": [
    "S. Brendle"
  ],
  "comment": "Final version, to appear in Invent. Math",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \\kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-02-03T21:27:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-similar solutions",
      "ricci flow",
      "rotational symmetry",
      "three-dimensional steady gradient ricci soliton",
      "perelmans first paper"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00222-013-0457-0",
      "journal": "Inventiones Mathematicae",
      "year": 2013,
      "month": "Dec",
      "volume": 194,
      "number": 3,
      "pages": 731
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013InMat.194..731B"
    }
  }
}