{
  "id": "2409.03070",
  "version": "v1",
  "published": "2024-09-04T20:44:22.000Z",
  "updated": "2024-09-04T20:44:22.000Z",
  "title": "Hausdorff measure and decay rate of Riesz capacity",
  "authors": [
    "Qiuling Fan",
    "Richard S. Laugesen"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-04T20:44:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B15"
    ],
    "keywords": [
      "riesz capacity",
      "decay rate",
      "yield hausdorff measure",
      "purely measure theoretic proof",
      "euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}