{
  "id": "2003.10194",
  "version": "v1",
  "published": "2020-03-23T11:42:12.000Z",
  "updated": "2020-03-23T11:42:12.000Z",
  "title": "$p$-Harmonic and Complex Isoparametric Functions on the Lie Groups $\\mathbb{R}^m \\ltimes \\mathbb{R}^n$ and $\\mathbb{R}^m \\ltimes \\mathrm{H}^{2n+1}$",
  "authors": [
    "Sigmundur Gudmundsson",
    "Marko Sobak"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we introduce the new notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper $p$-harmonic functions. We then apply this to construct the first known explicit proper $p$-harmonic functions on the Lie group semidirect products $\\mathbb{R}^m \\ltimes \\mathbb{R}^n$ and $\\mathbb{R}^m \\ltimes \\mathrm{H}^{2n+1}$, where $\\mathrm{H}^{2n+1}$ denotes the classical $(2n+1)$-dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-23T11:42:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B30",
      "53C43",
      "58E20"
    ],
    "keywords": [
      "complex isoparametric functions",
      "harmonic functions",
      "lie group semidirect products",
      "dimensional heisenberg group",
      "connected irreducible four-dimensional lie groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}