{
  "id": "1007.1400",
  "version": "v1",
  "published": "2010-07-08T15:10:54.000Z",
  "updated": "2010-07-08T15:10:54.000Z",
  "title": "Coupling of Brownian motions and Perelman's L-functional",
  "authors": [
    "Kazumasa Kuwada",
    "Robert Philipowski"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR",
    "math.DG"
  ],
  "abstract": "We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that the expectation of their normalized L-distance is non-increasing. As an immediate corollary we obtain a new proof of a recent result of Topping (J. reine angew. Math. 636 (2009), 93-122), namely that the normalized L-transportation cost between two solutions of the heat equation is non-increasing as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-08T15:10:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian motions",
      "perelmans l-functional",
      "riemannian metric evolves",
      "backwards ricci flow",
      "immediate corollary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.1400K"
    }
  }
}