{
  "id": "1706.01051",
  "version": "v1",
  "published": "2017-06-04T10:37:33.000Z",
  "updated": "2017-06-04T10:37:33.000Z",
  "title": "Equidistribution of expanding translates of curves in homogeneous spaces with the action of $(\\mathrm{SO}(n,1))^k$",
  "authors": [
    "Lei Yang"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a homogeneous space $X = G/\\Gamma$ with $G$ containing the group $H = (\\mathrm{SO}(n,1))^k$. Let $x\\in X$ such that $Hx$ is dense in $X$. Given an analytic curve $\\phi: I=[a,b] \\rightarrow H$, we will show that if $\\phi$ satisfies certain geometric condition, then for a typical diagonal subgroup $A =\\{a(t): t \\in \\mathbb{R}\\} \\subset H$ the translates $\\{a(t)\\phi(I)x: t >0\\}$ of the curve $\\phi(I)x$ will tend to be equidistributed in $X$ as $t \\rightarrow +\\infty$. The proof is based on the study of linear representations of $\\mathrm{SO}(n,1)$ and $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-04T10:37:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A17",
      "22E40",
      "37D40"
    ],
    "keywords": [
      "homogeneous space",
      "expanding translates",
      "equidistribution",
      "linear representations",
      "geometric condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}