{
  "abstract": "Let $Γ$ be a finitely generated hyperbolic group, and let $Q$ denote the conformal dimension of its Gromov boundary $\\partialΓ$. We prove that for every $p < \\frac{Q}{Q-1}$, the group $Γ$ admits a proper uniformly Lipschitz affine action on $\\ell^p$ with compression exponent $1/p$. The $\\ell^p$-space hosting the action is designed from a Markov chain on a specialized hyperbolic filling of $\\partialΓ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30583",
  "author_total": 2,
  "authors": [
    {
      "name": "Chris Gartland"
    },
    {
      "name": "Tianyi Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4gpc0n0vms5ne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30583",
  "fulltext_url": null,
  "id": "4gpc0n0vms5ne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30583",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
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  ],
  "openalex": "W7214617929",
  "pdf_url": "https://arxiv.org/pdf/2609.30583",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4gpc0n0vms5ne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30583",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30583"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Uniformly Lipschitz Hyperbolic Group Actions on $\\ell^p$",
  "title_text": "Uniformly Lipschitz Hyperbolic Group Actions on ℓ^p",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/4gpc0n0vms5ne",
  "venue": "arXiv",
  "versions": []
}