{
  "id": "1103.0314",
  "version": "v2",
  "published": "2011-03-01T23:32:15.000Z",
  "updated": "2013-09-02T17:29:57.000Z",
  "title": "Isoparametric hypersurfaces and metrics of constant scalar curvature",
  "authors": [
    "Guillermo Henry",
    "Jimmy Petean"
  ],
  "comment": "20 pages, to appear in The Assian Journal of Mathematics",
  "categories": [
    "math.DG"
  ],
  "abstract": "We showed the existence of non-radial solutions of the equation $\\Delta u -\\lambda u + \\lambda u^q =0$ on the round sphere $S^m$, for $q<2m/(m-2)$, and study the number of such solutions in terms of $\\lambda$. We show that for any isoparametric hypersurface $M\\subset S^m$ there are solutions such that $M$ is a regular level set (and the number of such solutions increases with $\\lambda$). We also show similar results for isoparametric hypersurfaces in general Riemannian manifolds. These solutions give multiplicity results for metrics of constant scalar curvature on conformal classes of Riemannian products.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-02T17:29:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21"
    ],
    "keywords": [
      "constant scalar curvature",
      "isoparametric hypersurface",
      "general riemannian manifolds",
      "regular level set",
      "round sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0314H"
    }
  }
}