{
  "id": "2007.01745",
  "version": "v1",
  "published": "2020-07-03T15:06:14.000Z",
  "updated": "2020-07-03T15:06:14.000Z",
  "title": "Good elliptic operators on Cantor sets",
  "authors": [
    "Guy David",
    "Svitlana Mayboroda"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that nonetheless there exist elliptic operators on (purely unrectifiable) Cantor sets in ${\\mathbb{R}}^2$ whose elliptic measure is absolutely continuous, and in fact, essentially proportional to the Hausdorff measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-03T15:06:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic operators",
      "cantor sets",
      "hausdorff measure",
      "harmonic measure",
      "elliptic measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}