{
  "id": "1802.03305",
  "version": "v1",
  "published": "2018-02-09T15:31:12.000Z",
  "updated": "2018-02-09T15:31:12.000Z",
  "title": "On Wasserstein isometries of probability measures on unit spheres",
  "authors": [
    "Dániel Virosztek"
  ],
  "categories": [
    "math.FA",
    "math-ph",
    "math.MG",
    "math.MP"
  ],
  "abstract": "We consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric $W_p$ for arbitrary $p \\geq 1.$ Our goal is to describe the isometry group of this metric space. We make some progress in the direction of a Banach-Stone-type result, that is, we show that the action of a Wasserstein isometry on the set of the Dirac measures is induced by an isometry of the underlying unit sphere. We also overview some of the recent results on isometries of measure spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-09T15:31:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E27",
      "54E40"
    ],
    "keywords": [
      "unit sphere",
      "wasserstein isometry",
      "borel probability measures",
      "euclidean space",
      "wasserstein metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}