{
  "id": "1111.2780",
  "version": "v1",
  "published": "2011-11-11T15:50:12.000Z",
  "updated": "2011-11-11T15:50:12.000Z",
  "title": "Square-integrability of solutions of the Yamabe equation",
  "authors": [
    "Bernd Ammann",
    "Mattias Dahl",
    "Emmanuel Humbert"
  ],
  "journal": "Comm. Anal. Geom. 21 (2013), no. 5, 891-916",
  "doi": "10.4310/CAG.2013.v21.n5.a2",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds which are bounded and L^p for p=2n/(n-2) are also L^2. This L^p-L^2-implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in a previous article of the authors. As an application we see that the smooth Yamabe invariant of any 2-connected compact 7-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions at least 11.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-11T15:50:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35P30",
      "57R65",
      "58J50",
      "58C40"
    ],
    "keywords": [
      "yamabe equation",
      "smooth yamabe invariant",
      "n-dimensional non-compact riemannian manifolds",
      "square-integrability",
      "explicit constants"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.2780A"
    }
  }
}