{
  "id": "2203.06232",
  "version": "v1",
  "published": "2022-03-11T20:18:42.000Z",
  "updated": "2022-03-11T20:18:42.000Z",
  "title": "A counterexample to the monotone increasing behavior of an Alt-Caffarelli-Friedman formula in the Heisenberg group",
  "authors": [
    "Fausto Ferrari",
    "Nicolò Forcillo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we provide a counterexample about the existence of an increasing monotonicity behavior of a function introduced in \\cite{FeFo}, companion of the celebrated Alt-Caffarelli-Friedman monotonicity formula, in the noncommutative framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-11T20:18:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R03",
      "35R35"
    ],
    "keywords": [
      "monotone increasing behavior",
      "heisenberg group",
      "alt-caffarelli-friedman formula",
      "counterexample",
      "celebrated alt-caffarelli-friedman monotonicity formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}