{
  "id": "2305.03492",
  "version": "v1",
  "published": "2023-05-05T13:07:28.000Z",
  "updated": "2023-05-05T13:07:28.000Z",
  "title": "The $p$-Laplacian overdetermined problem on Riemannian manifolds",
  "authors": [
    "Qihua Ruan",
    "Qin Huang",
    "Fan Chen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the overdetermined problem for the $p$-Laplacian equation on complete noncompact Riemannian manifolds with nonnegative Ricci curvature. We prove that the regularity results of weak solutions of the $p$-Laplacian equation and obtain some integral identities. As their applications, we give the proof of the $p$-Laplacian overdetermined problem and obtain some well known results such as the Heintze-Karcher inequality and the Soap Bubble Theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-05T13:07:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "laplacian overdetermined problem",
      "complete noncompact riemannian manifolds",
      "laplacian equation",
      "soap bubble theorem",
      "nonnegative ricci curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}