{
  "id": "2207.08411",
  "version": "v1",
  "published": "2022-07-18T07:13:32.000Z",
  "updated": "2022-07-18T07:13:32.000Z",
  "title": "Harmonic measures and rigidity for surface group actions on the circle",
  "authors": [
    "Masanori Adachi",
    "Yoshifumi Matsuda",
    "Hiraku Nozawa"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GT",
    "math.CV",
    "math.DG",
    "math.DS"
  ],
  "abstract": "Let $\\Gamma$ be a torsion-free lattice of $\\operatorname{PSU}(1,1)$. We study rigidity properties of $\\Gamma$-actions on the circle $S^1$ via foliated harmonic measures on the suspension bundles. We will show a curvature estimate and a Gauss-Bonnet formula for an $S^1$-connection obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of rigidity theorems of Matsumoto and Burger-Iozzi-Wienhard.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-18T07:13:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "surface group actions",
      "suspension bundle",
      "study rigidity properties",
      "maximal euler number",
      "suspension foliations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}