{
  "abstract": "We study a logarithmic re-gauging of the visual boundary, arising from the logarithmic metric on the sublinear Morse boundary introduced by Garg-Jana-Qing. For every proper geodesic hyperbolic space $X$, we prove that $d_{\\mathrm{log}}(ξ,η)\\asymp (1+(ξ\\midη)_o)^{-θ}$. As a consequence, under the natural identification of boundaries, $d_{\\mathrm{log}}$ is bi-Lipschitz equivalent to the polynomial Floyd boundary metric associated with the radial density $g_θ(t)=(1+t)^{-1-θ}$. Every quasi-isometry between proper geodesic hyperbolic spaces induces a bi-Lipschitz map between their logarithmic boundaries with a fixed admissible exponent. For every non-elementary hyperbolic group, the logarithmic boundary is nondoubling and has infinite Hausdorff and Assouad dimensions. Nevertheless, the logarithmic re-gauging preserves Nagata (capacity) dimension and continues to recover the asymptotic dimension of the group. It also detects one-endedness through linear connectedness (bounded turning) and preserves uniform perfectness. Thus the logarithmic and visual metrics are not quasisymmetrically equivalent, although several coarse-geometric features remain visible in the logarithmic boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25468",
  "author_total": 1,
  "authors": [
    {
      "name": "Manisha Garg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5dydhfjpgagrq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25468",
  "fulltext_url": null,
  "id": "5dydhfjpgagrq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25468",
  "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.GT"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214080801",
  "pdf_url": "https://arxiv.org/pdf/2609.25468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5dydhfjpgagrq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A new conformal gauge on the visual boundary of a hyperbolic group",
  "title_text": "A new conformal gauge on the visual boundary of a hyperbolic group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/5dydhfjpgagrq",
  "venue": "arXiv",
  "versions": []
}