{
  "id": "2010.00135",
  "version": "v1",
  "published": "2020-09-30T22:41:41.000Z",
  "updated": "2020-09-30T22:41:41.000Z",
  "title": "Blaschke-Santalo inequality for many functions and geodesic barycenters of measures",
  "authors": [
    "Alexander V. Kolesnikov",
    "Elisabeth M. Werner"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Motivated by the geodesic barycenter problem from optimal transportation theory, we prove a natural generalization of the Blaschke-Santalo inequality for many sets and many functions. We derive from it an entropy bound for the total Kantorovich cost appearing in the barycenter problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-30T22:41:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "blaschke-santalo inequality",
      "geodesic barycenter problem",
      "optimal transportation theory",
      "natural generalization",
      "entropy bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}