{
  "id": "2203.14833",
  "version": "v2",
  "published": "2022-03-28T15:14:23.000Z",
  "updated": "2022-04-04T17:57:58.000Z",
  "title": "On characterization of balls via solutions to the Helmholtz equation",
  "authors": [
    "Nikolay Kuznetsov"
  ],
  "comment": "6 pages, no figures, new material and references added",
  "categories": [
    "math.AP"
  ],
  "abstract": "A new analytical characterization of balls in the Euclidean space $\\RR^m$ is obtained. Unlike previous results of this kind, using either harmonic functions or solutions to the modified Helmholtz equation, the present one is based on solutions to the Helmholtz equation. This is achieved at the expense of a restriction imposed on the size of a domain -- a feature absent in the inverse mean value properties known before.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-04T17:57:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "inverse mean value properties",
      "modified helmholtz equation",
      "harmonic functions",
      "feature absent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}