{
  "id": "0906.2043",
  "version": "v1",
  "published": "2009-06-11T05:18:31.000Z",
  "updated": "2009-06-11T05:18:31.000Z",
  "title": "Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds",
  "authors": [
    "Genqian Liu"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we establish sharp inequalities for four kinds of classical eigenvalues on a bounded domain of a Riemannian manifold. We also establish asymptotic formulas for the eigenvalues of the buckling and clamped plate problems. In addition, we give a negative answer to the Payne conjecture for the one-dimensional case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-11T05:18:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "35P20",
      "58J50"
    ],
    "keywords": [
      "riemannian manifold",
      "eigenvalues",
      "clamped plate problems",
      "establish sharp inequalities",
      "one-dimensional case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2043L"
    }
  }
}