{
  "id": "math/0407530",
  "version": "v2",
  "published": "2004-07-30T12:28:01.000Z",
  "updated": "2004-11-29T15:13:47.000Z",
  "title": "Extremality for the Vafa-Witten bound on the sphere",
  "authors": [
    "Marc Herzlich"
  ],
  "comment": "to appear in G.A.F.A",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove that the round metric on the sphere has the largest first eigenvalue of the Dirac operator among all metrics that are larger than it. As a corollary, this gives an alternative proof of an extremality result for scalar curvature due to M. Llarull.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-11-29T15:13:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C27",
      "58J50",
      "58J60"
    ],
    "keywords": [
      "vafa-witten bound",
      "largest first eigenvalue",
      "scalar curvature",
      "round metric",
      "dirac operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7530H"
    }
  }
}