{
  "id": "0804.1717",
  "version": "v2",
  "published": "2008-04-10T14:26:05.000Z",
  "updated": "2009-06-25T08:09:11.000Z",
  "title": "The Yamabe problem with singularities",
  "authors": [
    "Farid Madani"
  ],
  "doi": "10.1016/j.bulsci.2007.09.004",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Let $(M,g)$ be a compact Riemannian manifold of dimension $n\\geq 3$. Under some assumptions, we prove that there exists a positive function $\\varphi$ solution of the following Yamabe type equation \\Delta \\varphi+ h\\varphi= \\tilde h \\varphi^{\\frac{n+2}{n-2}} where $h\\in L^p(M)$, $p>n/2$ and $\\tilde h\\in \\mathbb R$. We give the regularity of $\\varphi$ with respect to the value of $p$. Finally, we consider the results in geometry when $g$ is a singular Riemannian metric and $h=\\frac{n-2}{4(n-1)}R_g$, where $R_g$ is the scalar curvature of $g$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-25T08:09:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35J10"
    ],
    "keywords": [
      "yamabe problem",
      "singularities",
      "singular riemannian metric",
      "yamabe type equation",
      "compact riemannian manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1717M"
    }
  }
}