{
  "id": "1204.1268",
  "version": "v1",
  "published": "2012-04-05T16:19:36.000Z",
  "updated": "2012-04-05T16:19:36.000Z",
  "title": "Second Eigenvalue of the Yamabe Operator and Applications",
  "authors": [
    "Safaa El Sayed"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let $(M, g)$ be a compact Riemannian manifold of dimension $n \\geq 3$. In this paper, we give various properties of the eigenvalues of the Yamabe operator $L_g$. In particular, we show how the second eigenvalue of $L_g$ is related to the existence of nodal solutions of the equation $L_g u = \\epsilon | u|^{N-2} u$, where $\\epsilon = +1, 0,$ or -1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-05T16:19:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A30",
      "35J60",
      "35P30",
      "58J50",
      "58C40"
    ],
    "keywords": [
      "yamabe operator",
      "second eigenvalue",
      "applications",
      "compact riemannian manifold",
      "nodal solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.1268E"
    }
  }
}