{
  "id": "2305.01453",
  "version": "v1",
  "published": "2023-05-02T14:33:01.000Z",
  "updated": "2023-05-02T14:33:01.000Z",
  "title": "Nonlinear isocapacitary concepts of mass in nonnegative scalar curvature",
  "authors": [
    "Luca Benatti",
    "Mattia Fogagnolo",
    "Lorenzo Mazzieri"
  ],
  "categories": [
    "math.DG",
    "gr-qc",
    "math.AP"
  ],
  "abstract": "We deal with suitable nonlinear versions of Jauregui's Isocapacitary mass in $3$-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter $1<p\\leq 2$, interpolate between Jauregui's mass $p=2$ and Huisken's Isoperimetric mass, as $p \\to 1^+$. We derive Positive Mass Theorems for these masses under mild conditions at infinity, and we show that these masses do coincide with the $\\mathrm{ADM}$ mass when the latter is defined. We finally work out a nonlinear potential theoretic proof of the Penrose Inequality in the optimal asymptotic regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-02T14:33:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "83C99",
      "35B40",
      "35A16",
      "31C15",
      "53C21"
    ],
    "keywords": [
      "nonnegative scalar curvature",
      "nonlinear isocapacitary concepts",
      "compact outermost minimal boundary",
      "nonlinear potential theoretic proof",
      "optimal asymptotic regime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}