{
  "id": "1101.1226",
  "version": "v2",
  "published": "2011-01-06T14:35:16.000Z",
  "updated": "2011-03-14T11:22:46.000Z",
  "title": "A renormalized Perelman-functional and a lower bound for the ADM-mass",
  "authors": [
    "Robert Haslhofer"
  ],
  "comment": "8 pages (v2: announced mass decreasing flow in dimension three; minor additional improvements)",
  "journal": "J.Geom.Phys.61:2162-2167,2011",
  "doi": "10.1016/j.geomphys.2011.06.016",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "In the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning the regularity of Ricci-flat spaces and the non-uniqueness of the Ricci flow with conical initial data. In the second part, we define a geometric invariant lambda_AF for asymptotically flat manifolds with nonnegative scalar curvature. This invariant gives a quantitative lower bound for the ADM-mass from general relativity, motivates a Ricci flow proof of the rigidity statement in the positive mass theorem, and eventually leads to the discovery of a mass decreasing flow in dimension three.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-14T11:22:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "renormalized perelman-functional",
      "non-compact steady ricci solitons",
      "ricci flow proof",
      "short article"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Geometry and Physics",
      "year": 2011,
      "month": "Nov",
      "volume": 61,
      "number": 11,
      "pages": 2162
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 883496,
      "adsabs": "2011JGP....61.2162H"
    }
  }
}