{
  "abstract": "This paper introduces a general construction of self-similar metric spaces as a limit of discrete graphs. Our framework produces many classical examples, such as the Sierpiński carpet and the higher dimensional Menger sponges, but also a rich class of new examples. The main result of the work roughly speaking states: If the construction is sufficiently symmetric then the limiting object supports useful moduli estimates, namely the Combinatorial Loewner property of Bourdon–Kleiner and the super-multiplicativity inequality. We establish the super-multiplicativity on Menger sponges, for which it had not been previously known. The main new technique the work offers is a general framework of flows and resistance estimates on a rather general class of symmetric self-similar graphs.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, University of Jyväskylä, Seminaarinkatu 15, Jyväskylä, 40014, Finland"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Riku Anttila",
      "orcid": "0009-0008-4117-7677"
    },
    {
      "affs": [
        0
      ],
      "name": "Sylvester David Eriksson-Bique",
      "orcid": "0000-0002-1919-6475"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44x6pzmtcs7y4.bib",
  "cited_by": 11,
  "doi": "10.1007/s11118-026-10310-y",
  "fulltext_url": null,
  "id": "44x6pzmtcs7y4",
  "issns": [
    "0926-2601",
    "1572-929X"
  ],
  "landing_url": "https://doi.org/10.1007/s11118-026-10310-y",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7160988503",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s11118-026-10310-y.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-13",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/44x6pzmtcs7y4.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W7160988503",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s11118-026-10310-y"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Geometric Analysis and Curvature Flows",
      "subfield": "general"
    }
  ],
  "title": "The Combinatorial Loewner Property and Super-Multiplicativity Inequalities for Symmetric Self-Similar Metric Spaces",
  "title_text": "The Combinatorial Loewner Property and Super-Multiplicativity Inequalities for Symmetric Self-Similar Metric Spaces",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/44x6pzmtcs7y4",
  "venue": "Potential Analysis",
  "versions": []
}