{
  "id": "math/9806081",
  "version": "v1",
  "published": "1998-06-15T12:49:27.000Z",
  "updated": "1998-06-15T12:49:27.000Z",
  "title": "Upper bounds for the first eigenvalue of the Dirac operator on surfaces",
  "authors": [
    "Ilka Agricola",
    "Thomas Friedrich"
  ],
  "comment": "Latex2.09, 23 pages",
  "doi": "10.1016/S0393-0440(98)00032-1",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface $M^2 \\hookrightarrow {\\Bbb R}^3$ as well as intrinsic bounds for 2-dimensional compact manifolds of genus zero and genus one. Moreover, we compare the different estimates of the eigenvalue of the Dirac operator for special families of metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-06-15T12:49:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58G25",
      "53A05"
    ],
    "keywords": [
      "dirac operator",
      "first eigenvalue",
      "extrinsic upper bounds",
      "compact manifolds",
      "intrinsic bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}