{
  "id": "2211.06939",
  "version": "v1",
  "published": "2022-11-13T16:19:52.000Z",
  "updated": "2022-11-13T16:19:52.000Z",
  "title": "Monotone quantities of $p$-harmonic functions and their applications",
  "authors": [
    "Sven Hirsch",
    "Pengzi Miao",
    "Luen-Fai Tam"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.DG",
    "gr-qc",
    "math.AP"
  ],
  "abstract": "We derive local and global monotonic quantities associated to $p$-harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the $p$-capacity and the Willmore functional of the boundary. As $ p \\to 1$, one of the results retrieves a classic relation that the ADM mass dominates the Hawking mass if the surface is area outer-minimizing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-13T16:19:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic functions",
      "monotone quantities",
      "applications",
      "adm mass dominates",
      "global monotonic quantities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}