{
  "id": "2111.12752",
  "version": "v2",
  "published": "2021-11-24T19:27:02.000Z",
  "updated": "2022-01-28T13:08:22.000Z",
  "title": "Uniqueness of conformal measures and local mixing for Anosov groups",
  "authors": [
    "Sam Edwards",
    "Minju Lee",
    "Hee Oh"
  ],
  "comment": "17 pages, To appear in Michigan Mathematical Journal (Prasad volume)",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "In the late seventies, Sullivan showed that for a convex cocompact subgroup $\\Gamma$ of $\\operatorname{SO}^\\circ(n,1)$ with critical exponent $\\delta>0$, any $\\Gamma$-conformal measure on $\\partial \\mathbb{H}^n$ of dimension $\\delta$ is necessarily supported on the limit set $\\Lambda$ and that the conformal measure of dimension $\\delta$ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup of a connected semisimple real algebraic group $G$ of rank at most $3$. We also obtain the local mixing for generalized BMS measures on $\\Gamma\\backslash G$ including Haar measures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-01-28T13:08:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal measure",
      "anosov groups",
      "local mixing",
      "uniqueness",
      "zariski dense anosov subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}