{
  "id": "0906.0927",
  "version": "v3",
  "published": "2009-06-04T19:12:04.000Z",
  "updated": "2010-12-23T15:43:58.000Z",
  "title": "A compactness theorem for scalar-flat metrics on manifolds with boundary",
  "authors": [
    "Sergio Almaraz"
  ],
  "comment": "49 pages. Final version, to appear in Calc. Var. Partial Differential Equations",
  "journal": "Calc. Var. Partial Differential Equations 41(3), 341-386 (2011)",
  "doi": "10.1007/s00526-010-0365-8",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-12-23T15:43:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35J65"
    ],
    "keywords": [
      "scalar-flat metrics",
      "compactness theorem",
      "constant mean curvature hypersurface",
      "trace-free 2nd fundamental form",
      "compact riemannian manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0927A"
    }
  }
}