{
  "id": "math/0304043",
  "version": "v3",
  "published": "2003-04-03T13:33:25.000Z",
  "updated": "2008-02-25T16:55:24.000Z",
  "title": "Positive mass theorem for the Yamabe problem on spin manifolds",
  "authors": [
    "Bernd Ammann",
    "Emmanuel Humbert"
  ],
  "comment": "A term is missing in Version 2 and the printed version. The term is added in Version 3",
  "journal": "GAFA 15 (2005), 567-576",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let $(M,g)$ be a compact connected spin manifold of dimension $n\\geq 3$ whose Yamabe invariant is positive. We assume that $(M,g)$ is locally conformally flat or that $n \\in \\{3,4,5\\}$. According to a positive mass theorem of Witten, the constant term in the asymptotic development of the Green's function of the conformal Laplacian is positive if $(M,g)$ is not conformally equivalent to the sphere. In the present article, we will give a proof for this fact which is considerably shorter than previous proofs. Our proof is a modification of Witten's argument, but no analysis on asymtotically flat spaces is needed.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-02-25T16:55:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "58E11",
      "53C27"
    ],
    "keywords": [
      "positive mass theorem",
      "yamabe problem",
      "compact connected spin manifold",
      "flat spaces",
      "wittens argument"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4043A"
    }
  }
}