{
  "id": "2406.10781",
  "version": "v1",
  "published": "2024-06-16T02:38:59.000Z",
  "updated": "2024-06-16T02:38:59.000Z",
  "title": "Riesz capacity: monotonicity, continuity, diameter and volume",
  "authors": [
    "Carrie Clark",
    "Richard S. Laugesen"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Properties of Riesz capacity are developed with respect to the kernel exponent $p \\in (-\\infty,n)$, namely that capacity is monotonic as a function of $p$, that its endpoint limits recover the diameter and volume of the set, and that capacity is left-continuous with respect to $p$ and is right-continuous provided (when $p \\geq 0$) that an additional hypothesis holds. Left and right continuity properties of the equilibrium measure are obtained too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-16T02:38:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31A15",
      "31B15"
    ],
    "keywords": [
      "riesz capacity",
      "monotonicity",
      "additional hypothesis holds",
      "right continuity properties",
      "equilibrium measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}