{
  "id": "math/0301350",
  "version": "v3",
  "published": "2003-01-30T04:01:32.000Z",
  "updated": "2003-06-09T18:15:10.000Z",
  "title": "A fully nonlinear equation on 4-manifolds with positive scalar curvature",
  "authors": [
    "Matthew Gursky",
    "Jeff Viaclovsky"
  ],
  "comment": "20 pages; to appear in Journal of Differential Geometry",
  "journal": "Final version: Journal of Differential Geometry 63, no. 1, 2003, 131-154",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We present a conformal deformation involving a fully nonlinear equation in dimension 4, starting with positive scalar curvature. Assuming a certain conformal invariant is positive, one may deform from positive scalar curvature to a stronger condition involving the Ricci tensor. We also give a new conformally invariant condition for positivity of the Paneitz operator, which allows us to give many new examples of manifolds admitting metrics with constant $Q$-curvature.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-06-09T18:15:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53A30"
    ],
    "keywords": [
      "positive scalar curvature",
      "fully nonlinear equation",
      "conformal deformation",
      "conformal invariant",
      "manifolds admitting metrics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1350G"
    }
  }
}