{
  "id": "1607.08306",
  "version": "v1",
  "published": "2016-07-28T03:39:27.000Z",
  "updated": "2016-07-28T03:39:27.000Z",
  "title": "Partial result of Yau's Conjecture of the first eigenvalue in unit sphere $\\mathbb{S}^{n+1}(1)$",
  "authors": [
    "Zhongyang Sun"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we partially solve Yau' Conjecture of the first eigenvalue of an embedded compact minimal hypersurface of unit sphere $\\mathbb{S}^{n+1}(1)$, i.e., Corollary 1.2. In particular, Corollary 1.3 proves that the condition $\\int_{\\Omega_{1}}|\\nabla u|^{2}=(n+1)\\int_{\\Omega_{1}}u^{2}$ is naturally true and meaningful in Corollary 1.2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-28T03:39:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first eigenvalue",
      "unit sphere",
      "yaus conjecture",
      "partial result",
      "embedded compact minimal hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}