{
  "id": "1111.6663",
  "version": "v1",
  "published": "2011-11-29T01:49:08.000Z",
  "updated": "2011-11-29T01:49:08.000Z",
  "title": "General estimate of the first eigenvalue on manifolds",
  "authors": [
    "Mu-Fa Chen"
  ],
  "comment": "19 pages",
  "journal": "Front. Math. China 2011, 6(6): 1025-1043",
  "categories": [
    "math.PR",
    "math.DG",
    "math.SP"
  ],
  "abstract": "Ten sharp lower estimates of the first non-trivial eigenvalue of Laplacian on compact Riemannian manifolds are reviewed and compared. An improved variational formula, a general common estimate, and a new sharp one are added. The best lower estimates are now updated. The new estimates provide a global picture of what one can expect by our approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-29T01:49:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58C40",
      "35P15"
    ],
    "keywords": [
      "first eigenvalue",
      "general estimate",
      "first non-trivial eigenvalue",
      "best lower estimates",
      "general common estimate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6663C"
    }
  }
}