{
  "id": "0711.3859",
  "version": "v2",
  "published": "2007-11-24T22:04:33.000Z",
  "updated": "2009-03-05T22:55:31.000Z",
  "title": "Convergence and stability of locally \\mathbb{R}^{N}-invariant solutions of Ricci flow",
  "authors": [
    "Dan Knopf"
  ],
  "comment": "The only revisions are improvements in exposition and notation. To appear in Journal of Geometric Analysis",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Important models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally G-invariant solutions on principal bundles, where G is a nilpotent Lie group. In this paper, we establish convergence and asymptotic stability, modulo smooth finite-dimensional center manifolds, of certain R^{N}-invariant solutions. When the dimension of the total space is three, these results are relevant to work of Lott classifying the asymptotic behavior of all 3-dimensional Ricci flow solutions whose sectional curvatures and diameters are respectively O(t^{-1}) and O(t^{1/2}).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-05T22:55:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "58J37"
    ],
    "keywords": [
      "convergence",
      "modulo smooth finite-dimensional center manifolds",
      "nilpotent lie group",
      "ricci flow solutions",
      "asymptotic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3859K"
    }
  }
}