{
  "abstract": "This is the higher dimensional continuation of our works on Hausdorff dimension of Kleinian groups \\cite{Hou2010}, \\cite{Hou2020}. In this paper we prove that for all $r\\ge 2$ there exists $λ_r>0$, which is independent of the dimension $N$ of the hyperbolic space, such that any finitely generated non-elementary torsion-free Kleinian group of $\\Isom(\\mathbb{H}^N)$ generated by $r$ elements with limit set of Hausdorff dimension $<λ_r$ is a classical Schottky group. For two generators the bound can be taken to be $1/3$. The proof relies on our previous works in \\cite{Hou2010}, \\cite{Hou2020} and on a metric carrier graph reduction. Our result can also be considered as the complete converse to the well-known theorem of Phillips-Sarnak \\cite{PS} for spaces of any dimension $N$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03335",
  "author_total": 1,
  "authors": [
    {
      "name": "Yong Hou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ttgeg64gcta5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03335",
  "fulltext_url": null,
  "id": "7ttgeg64gcta5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03335",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03335",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ttgeg64gcta5.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03335",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03335"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higher dimensional Kleinian groups of small Hausdorff dimension are classical Schottky groups II",
  "title_text": "Higher dimensional Kleinian groups of small Hausdorff dimension are classical Schottky groups II",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/7ttgeg64gcta5",
  "venue": "arXiv",
  "versions": []
}