{
  "id": "1710.09519",
  "version": "v1",
  "published": "2017-10-26T03:02:43.000Z",
  "updated": "2017-10-26T03:02:43.000Z",
  "title": "Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds",
  "authors": [
    "Bingqing Ma",
    "Guangyue Huang"
  ],
  "comment": "All comments are welcome",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this short note, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $$\\Delta u+\\lambda u^{p}=0,$$ where $\\lambda,p$ are two real constants and $\\lambda\\neq 0$. As an application, a Liouville type result is attained in some appropriate conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-26T03:02:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear elliptic equation",
      "complete riemannian manifold",
      "gradient estimates",
      "liouville type result",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}