{
  "id": "1807.08406",
  "version": "v1",
  "published": "2018-07-23T02:32:33.000Z",
  "updated": "2018-07-23T02:32:33.000Z",
  "title": "A compactness theorem for scalar-flat metrics on 3-manifolds with boundary",
  "authors": [
    "Sergio Almaraz",
    "Olivaine S. de Queiroz",
    "Shaodong Wang"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. This involves a blow-up analysis of a Yamabe-type equation with critical Sobolev exponent on the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-23T02:32:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35J65"
    ],
    "keywords": [
      "scalar-flat metrics",
      "compactness theorem",
      "compact riemannian three-dimensional manifold",
      "constant mean curvature hypersurface",
      "blow-up analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}