{
  "id": "1103.1543",
  "version": "v4",
  "published": "2011-03-08T14:47:27.000Z",
  "updated": "2011-08-29T14:00:52.000Z",
  "title": "Mass transport and uniform rectifiability",
  "authors": [
    "Xavier Tolsa"
  ],
  "comment": "Minor corrections and adjustments. To appear in Geom. Funct. Anal",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "In this paper we characterize the so called uniformly rectifiable sets of David and Semmes in terms of the Wasserstein distance $W_2$ from optimal mass transport. To obtain this result, we first prove a localization theorem for the distance $W_2$ which asserts that if $\\mu$ and $\\nu$ are probability measures in $R^n$, $\\phi$ is a radial bump function smooth enough so that $\\int\\phi d\\mu\\gtrsim1$, and $\\mu$ has a density bounded from above and from below on the support of \\phi, then $W_2(\\phi\\mu,a\\phi\\nu)\\leq c W_2(\\mu,\\nu),$ where $a=\\int\\phi d\\mu/ \\int\\phi\\,d\\nu$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-08-29T14:00:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "49Q20"
    ],
    "keywords": [
      "uniform rectifiability",
      "radial bump function smooth",
      "optimal mass transport",
      "probability measures",
      "wasserstein distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1543T"
    }
  }
}