{
  "id": "1503.08493",
  "version": "v1",
  "published": "2015-03-29T20:47:05.000Z",
  "updated": "2015-03-29T20:47:05.000Z",
  "title": "Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces",
  "authors": [
    "Mikhail A. Karpukhin"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DG",
    "math.SP"
  ],
  "abstract": "In 1980 Yang and Yau~\\cite{YY} proved the celebrated upper bound for the first eigenvalue on an orientable surface of genus $\\gamma$. Later Li and Yau~\\cite{LY} gave a simple proof of this bound by introducing the concept of conformal volume of a Riemannian manifold. In the same paper they proposed an approach for obtaining a similar estimate for non-orientable surfaces. In the present paper we formalize their argument and improve the bounds stated in~\\cite{LY}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-29T20:47:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E11",
      "58J50",
      "35P15"
    ],
    "keywords": [
      "first eigenvalue",
      "non-orientable surfaces",
      "celebrated upper bound",
      "simple proof",
      "conformal volume"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}