{
  "id": "0901.0422",
  "version": "v1",
  "published": "2009-01-05T05:24:51.000Z",
  "updated": "2009-01-05T05:24:51.000Z",
  "title": "Einstein and conformally flat critical metrics of the volume functional",
  "authors": [
    "Pengzi Miao",
    "Luen-Fai Tam"
  ],
  "comment": "38 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let $R$ be a constant. Let $\\mathcal{M}^R_\\gamma$ be the space of smooth metrics $g$ on a given compact manifold $\\Omega^n$ ($n\\ge 3$) with smooth boundary $\\Sigma $ such that $g$ has constant scalar curvature $R$ and $g|_{\\Sigma}$ is a fixed metric $\\gamma$ on $\\Sigma$. Let $V(g)$ be the volume of $g\\in\\mathcal{M}^R_\\gamma$. In this work, we classify all Einstein or conformally flat metrics which are critical points of $V(\\cdot)$ in $\\mathcal{M}^R_\\gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-05T05:24:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "conformally flat critical metrics",
      "volume functional",
      "constant scalar curvature",
      "compact manifold",
      "smooth boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}