{
  "id": "1602.03610",
  "version": "v1",
  "published": "2016-02-11T03:08:46.000Z",
  "updated": "2016-02-11T03:08:46.000Z",
  "title": "Upper bounds on the first eigenvalue for the $p$-Laplacian",
  "authors": [
    "Guangyue Huang",
    "Zhi Li"
  ],
  "comment": "All comments are welcome",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we establish gradient estimates for positive solutions to the following equation with respect to the $p$-Laplacian $$\\Delta_{p}u=-\\lambda |u|^{p-2}u$$ with $p>1$ on a given complete Riemannian manifold. Consequently, we derive upper bound estimates of the first nontrivial eigenvalue of the $p$-Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-11T03:08:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first eigenvalue",
      "derive upper bound estimates",
      "first nontrivial eigenvalue",
      "complete riemannian manifold",
      "establish gradient estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160203610H"
    }
  }
}