{
  "id": "math/0003068",
  "version": "v1",
  "published": "2000-03-13T14:05:12.000Z",
  "updated": "2000-03-13T14:05:12.000Z",
  "title": "Ricci Curvature, Minimal Volumes, and Seiberg-Witten Theory",
  "authors": [
    "Claude LeBrun"
  ],
  "comment": "41 pages, LaTeX2e",
  "doi": "10.1007/s002220100148",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4-manifold minimizes volume among all metrics satisfying a point-wise lower bound on sectional curvature plus suitable multiples of the scalar curvature. These estimates also imply new non-existence results for Einstein metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-13T14:05:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci curvature",
      "minimal volumes",
      "seiberg-witten theory",
      "sectional curvature plus suitable multiples",
      "sharp lower bounds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2001,
      "month": "Aug",
      "volume": 145,
      "number": 2,
      "pages": 279
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 525226,
      "adsabs": "2001InMat.145..279L"
    }
  }
}