{
  "id": "2103.09268",
  "version": "v1",
  "published": "2021-03-16T18:24:17.000Z",
  "updated": "2021-03-16T18:24:17.000Z",
  "title": "Every 2-dimensional Banach space has the Mazur-Ulam property",
  "authors": [
    "Taras Banakh"
  ],
  "comment": "8 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We prove that every isometry between the unit spheres of 2-dimensional Banach spaces extends to a linear isometry of the Banach spaces. This resolves the famous Tingley's problem in the class of 2-dimensional Banach spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-16T18:24:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "52A21",
      "52A10",
      "53A04",
      "54E35",
      "54E40"
    ],
    "keywords": [
      "mazur-ulam property",
      "banach spaces extends",
      "unit spheres",
      "famous tingleys problem",
      "linear isometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}