{
  "id": "1605.03850",
  "version": "v1",
  "published": "2016-05-12T15:04:35.000Z",
  "updated": "2016-05-12T15:04:35.000Z",
  "title": "The Myers-Steenrod theorem for Finsler manifolds of low regularity",
  "authors": [
    "Vladimir S. Matveev",
    "Marc Troyanov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove a version of Myers-Steenrod's theorem for Finsler manifolds under minimal regularity hypothesis. In particular we show that an isometry between $C^{k,\\alpha}$-smooth (or partially smooth) Finsler metrics, with $k+\\alpha>0$, $k\\in \\mathbb{N} \\cup \\{0\\}$, and $0 \\leq \\alpha \\leq 1$ is necessary a diffeomorphism of class $C^{k+1,\\alpha}$. A generalisation of this result to the case of Finsler 1-quasiconformal mapping is given. The proofs are based on the reduction of the Finlserian problems to Riemannian ones with the help of the the Binet-Legendre metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-12T15:04:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B40",
      "53C60",
      "35B65"
    ],
    "keywords": [
      "finsler manifolds",
      "low regularity",
      "myers-steenrod theorem",
      "minimal regularity hypothesis",
      "myers-steenrods theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}