{
  "id": "0909.0716",
  "version": "v2",
  "published": "2009-09-03T17:15:14.000Z",
  "updated": "2011-07-31T16:17:21.000Z",
  "title": "On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below",
  "authors": [
    "Shijin Zhang"
  ],
  "comment": "15 pages. Added some references and an appendix to give a more simple computation of the volume estimate",
  "journal": "Acta Mathematica Sinica, Einglish series. vol. 27, 2011, 871-882",
  "doi": "10.1007/s10114-011-9527-7",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct (elliptic) proof of this sharp estimate. Moreover, if the scalar curvature attains its minimum value at some point, then the manifold is Einstein.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-31T16:17:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "sharp volume estimate",
      "scalar curvature",
      "sharp estimate",
      "complete gradient ricci solitons",
      "local lower bound estimate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0716Z"
    }
  }
}