{
  "id": "1612.01255",
  "version": "v1",
  "published": "2016-12-05T06:06:08.000Z",
  "updated": "2016-12-05T06:06:08.000Z",
  "title": "The First Eigenvalue for the Bi-Beltrami-Laplacian on Minimal Isoparametric Hypersurfaces of $\\mathbb{S}^{n+1}(1)$",
  "authors": [
    "Lingzhong Zeng"
  ],
  "comment": "5 pages",
  "categories": [
    "math.DG",
    "math.SP"
  ],
  "abstract": "In this paper, we investigate the first eigenvalues of two closed eigenvalue problems of the bi-Beltrami-Laplacian on minimal embedded isoparametric hypersurface in the unit sphere $\\mathbb{S}^{n+1}(1)$. Although many mathematicians want to derive the corresponding results for the first eigenvalues of bi-Beltrami-Laplacian, they encountered great difficulties in proving the limit theorem of the version of bi-Beltrami-Laplacian along with the strategy due to I. Chavel and E. A. Feldman(Journal of Functional Analysis, 30 (1978), 198-222) and S. Ozawa (Duke Mathematics Journal, 48 (1981),767-778). Therefore, as the author knows, there are no any results of Tang-Yan type( Journal of Differential Geometry, 94 (2013) 521-540). However, by the variational argument, we overcome the difficulties and determine the first eigenvalues of the bi-Beltrami-Laplacian in the sense of isoparametric hypersurfaces. We note that our proof is quite simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-05T06:06:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first eigenvalue",
      "minimal isoparametric hypersurfaces",
      "bi-beltrami-laplacian",
      "minimal embedded isoparametric hypersurface",
      "duke mathematics journal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}