{
  "id": "1310.0658",
  "version": "v4",
  "published": "2013-10-02T11:00:11.000Z",
  "updated": "2014-12-16T22:56:35.000Z",
  "title": "Uniform measures and uniform rectifiability",
  "authors": [
    "Xavier Tolsa"
  ],
  "comment": "Minor corrections",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "In this paper it is shown that if $\\mu$ is an n-dimensional Ahlfors-David regular measure in $R^d$ which satisfies the so-called weak constant density condition, then $\\mu$ is uniformly rectifiable. This had already been proved by David and Semmes in the cases n=1, 2 and d-1, and it was an open problem for other values of n. The proof of this result relies on the study of the n-uniform measures in $R^d$. In particular, it is shown here that they satisfy the \"big pieces of Lipschitz graphs\" property.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-02-09T19:05:55.000Z",
      "comment": "Corrections in the statements of Lemmas 3.2 and 3.3, which do not affect the rest of the paper",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-12-16T22:56:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "49Q15"
    ],
    "keywords": [
      "uniform rectifiability",
      "n-dimensional ahlfors-david regular measure",
      "weak constant density condition",
      "big pieces",
      "n-uniform measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0658T"
    }
  }
}