{
  "abstract": "We study the Ahlfors-regular conformal dimension of spaces with locally expanding self-covering maps and, more generally, limit spaces of contracting self-similar groups. We show that the conformal dimension is characterized by combinatorial moduli associated with the Schreier graphs of these groups. We compare these moduli with contraction coefficients of self-similar group actions and with algebras of functions on the limit spaces satisfying asymptotic $p$-energy conditions. We also give conditions on the group when the conformal dimension is equal to the infimum of visual metrics on the self-similarity complex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19260",
  "author_total": 1,
  "authors": [
    {
      "name": "Volodymyr Nekrashevych"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ax9vzy7dscgms.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19260",
  "fulltext_url": null,
  "id": "ax9vzy7dscgms",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19260",
  "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.GR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  ],
  "openalex": "W7222335126",
  "pdf_url": "https://arxiv.org/pdf/2610.19260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ax9vzy7dscgms.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Conformal dimension and self-similar groups",
  "title_text": "Conformal dimension and self-similar groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/ax9vzy7dscgms",
  "venue": "arXiv",
  "versions": []
}