{
  "id": "2203.06794",
  "version": "v1",
  "published": "2022-03-14T00:17:59.000Z",
  "updated": "2022-03-14T00:17:59.000Z",
  "title": "Dichotomy and measures on limit sets of Anosov groups",
  "authors": [
    "Minju Lee",
    "Hee Oh"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let $G$ be a connected semisimple real algebraic group. For any Zariski dense Anosov subgroup $\\Gamma <G$, we show that a $\\Gamma$-conformal measure is supported on the limit set of $\\Gamma$ if and only if its \"dimension\" is $\\Gamma$-critical. This implies the uniqueness of a $\\Gamma$-conformal measure for each critical dimension. We deduce this from a higher rank analogue of the Hopf-Tsuji-Sullivan dichotomy for the maximal diagonal action. Other applications include an analogue of the Ahlfors measure conjecture for Anosov subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-14T00:17:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limit set",
      "anosov groups",
      "conformal measure",
      "zariski dense anosov subgroup",
      "connected semisimple real algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}