{
  "id": "1003.2107",
  "version": "v1",
  "published": "2010-03-10T13:28:10.000Z",
  "updated": "2010-03-10T13:28:10.000Z",
  "title": "Stability of hyperbolic space under Ricci flow",
  "authors": [
    "Oliver C. Schnürer",
    "Felix Schulze",
    "Miles Simon"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and higher, the scaled Ricci harmonic map heat flow of such a metric converges smoothly, uniformly and exponentially fast in all C^k-norms and in the L^2-norm to the hyperbolic metric as time approaches infinity. We also prove a related result for the Ricci flow and for the two-dimensional conformal Ricci flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-10T13:28:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35B35"
    ],
    "keywords": [
      "hyperbolic space",
      "ricci harmonic map heat flow",
      "scaled ricci harmonic map heat",
      "hyperbolic metric",
      "two-dimensional conformal ricci flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2107S"
    }
  }
}