{
  "id": "2008.03969",
  "version": "v1",
  "published": "2020-08-10T09:06:41.000Z",
  "updated": "2020-08-10T09:06:41.000Z",
  "title": "Convergence of Ricci flow solutions to Taub-NUT",
  "authors": [
    "Francesco Di Giovanni"
  ],
  "comment": "48 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric $g_{0}$ on $\\mathbb{R}^{4}$ with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If $g_{0}$ has bounded Hopf-fiber, curvature controlled by the size of the orbits and opens faster than a paraboloid in the directions orthogonal to the Hopf-fiber, then the flow converges to the Taub-NUT metric $g_{\\mathsf{TNUT}}$ in the Cheeger-Gromov sense in infinite time. We also classify the long-time behaviour when $g_{0}$ is asymptotically flat. In order to identify infinite-time singularity models we obtain a uniqueness result for $g_{\\mathsf{TNUT}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-10T09:06:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci flow solutions",
      "convergence",
      "identify infinite-time singularity models",
      "uniqueness result",
      "monotone warping coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}