{
  "id": "1507.00053",
  "version": "v1",
  "published": "2015-06-30T22:28:51.000Z",
  "updated": "2015-06-30T22:28:51.000Z",
  "title": "Solutions to the singular $σ_2-$Yamabe problem with isolated singularities",
  "authors": [
    "Almir Silva Santos"
  ],
  "comment": "35 pages. arXiv admin note: text overlap with arXiv:0911.4477",
  "categories": [
    "math.DG"
  ],
  "abstract": "Given $(M,g_0)$ a closed Riemannian manifold and a nonempty closed subset $X$ in $M$, the singular $\\sigma_k-$Yamabe problem asks for a complete metric $g$ on $M\\backslash X$ conformal to $g_0$ with constant $\\sigma_k-$curvature. The $\\sigma_k-$curvature is defined as the $k-$th elementary symmetric function of the eigenvalues of the Schouten tensor of a Riemannian metric. The main goal of this paper is to find solutions to the singular $\\sigma_2-$Yamabe problem with isolated singularities in any compact non-degenerate manifold such that the Weyl tensor vanishing to sufficiently high order at the singular point. We will use perturbation techniques and gluing methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-30T22:28:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "53A30"
    ],
    "keywords": [
      "isolated singularities",
      "th elementary symmetric function",
      "compact non-degenerate manifold",
      "yamabe problem asks",
      "schouten tensor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150700053S"
    }
  }
}