{
  "id": "1910.01862",
  "version": "v1",
  "published": "2019-10-04T10:38:27.000Z",
  "updated": "2019-10-04T10:38:27.000Z",
  "title": "Stability estimates for the conformal group of $\\mathbb{S}^{n-1}$ in dimension $n\\geq 3$",
  "authors": [
    "Stephan Luckhaus",
    "Konstantinos Zemas"
  ],
  "comment": "38 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "The purpose of this paper is to exhibit a quantitative stability result for the class of M\\\"obius transformations of $\\mathbb{S}^{n-1}$ when $n\\geq 3$. The main estimate is of local nature and asserts that for a Lipschitz map that is apriori close to a M\\\"obius transformation, an average conformal-isoperimetric type of deficit controls the deviation (in an average sense) of the map in question from a particular M\\\"obius map. The optimality of the result together with its link with the geometric rigidity of the special orthogonal group are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-04T10:38:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C70"
    ],
    "keywords": [
      "conformal group",
      "stability estimates",
      "special orthogonal group",
      "average conformal-isoperimetric type",
      "stability result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}