{
  "id": "1908.06420",
  "version": "v1",
  "published": "2019-08-18T10:40:05.000Z",
  "updated": "2019-08-18T10:40:05.000Z",
  "title": "Poincaré Inequalities and Uniform Rectifiability",
  "authors": [
    "Jonas Azzam"
  ],
  "categories": [
    "math.CA",
    "math.DG",
    "math.MG"
  ],
  "abstract": "We show that any $d$-Ahlfors regular subset of $\\mathbb{R}^{n}$ supporting a weak $(1,d)$-Poincar\\'e inequality with respect to surface measure is uniformly rectifiable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-18T10:40:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "28A78",
      "28A12",
      "46E35",
      "49J52",
      "53C23"
    ],
    "keywords": [
      "uniform rectifiability",
      "ahlfors regular subset",
      "poincare inequality",
      "surface measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}