{
  "id": "1005.3345",
  "version": "v3",
  "published": "2010-05-19T00:41:04.000Z",
  "updated": "2010-07-26T02:55:26.000Z",
  "title": "On the Unboundedness of the First Eigenvalue of the Laplacian for G-Invariant Metrics",
  "authors": [
    "Paul Cernea"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this note we partially answer a question posed by Colbois, Dryden, and El Soufi. Consider the space of constant-volume Riemannian metrics on a connected manifold M which are invariant under the action of a discrete Lie group G. We show that the first eigenvalue of the Laplacian is not bounded above on this space, provided M = S^n, G acts freely, and S^n/G with the round metric admits a Killing vector field of constant length, or provided M is a compact Lie group not equal to T^n, and G is a discrete subgroup of M.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-07-26T02:55:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first eigenvalue",
      "g-invariant metrics",
      "unboundedness",
      "constant-volume riemannian metrics",
      "round metric admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.3345C"
    }
  }
}