{
  "id": "1911.07991",
  "version": "v1",
  "published": "2019-11-18T22:41:24.000Z",
  "updated": "2019-11-18T22:41:24.000Z",
  "title": "Smooth semi-Lipschitz functions and almost isometries of Finsler manifolds",
  "authors": [
    "Aris Daniilidis",
    "Jesus Jaramillo",
    "Francisco Venegas M"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The convex cone $SC_{\\mathrm{SLip}}^1(\\mathcal{X})$ of real-valued smooth semi-Lipschitz functions on a Finsler manifold $\\mathcal{X}$ is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of $\\mathcal{X}$. In this work we show that the subset of smooth semi-Lipschitz functions of constant strictly less than $1$, denoted $SC_{1^{-}}^1(\\mathcal{X})$, can be used to classify Finsler manifolds and to characterize almost isometries between them, in the lines of the classical Banach-Stone and Mykers-Nakai theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-18T22:41:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C40",
      "54C65"
    ],
    "keywords": [
      "isometries",
      "real-valued smooth semi-lipschitz functions",
      "quasi-metric feature",
      "order-algebraic structure",
      "mykers-nakai theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}