{
  "abstract": "We study the relationship between the large-scale geometry of a geodesic metric space and the slimness of its geodesic polygons. We show that if there is a uniform constant $δ$ such that every geodesic polygon in an unbounded geodesic metric space is $δ$-slim, then the space has asymptotic Assouad--Nagata dimension one. We further consider graphs of bounded valency and allow the slimness constant of an $n$-gon to grow logarithmically with $n$. More precisely, under an explicit logarithmic bound on the slimness of geodesic $n$-gons, we prove that the graph has asymptotic Assouad--Nagata dimension one. Thus, sufficiently strong logarithmic control on the slimness of geodesic polygons forces one-dimensional large-scale geometry. We also obtain two criteria for graphs, outside the hyperbolic setting, to have asymptotic Assouad--Nagata dimension one. In particular, these criteria show that one-dimensional large-scale geometry can be detected from quantitative restrictions on the slimness of geodesic polygons, without requiring the space to be hyperbolic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05429",
  "author_total": 1,
  "authors": [
    {
      "name": "Panagiotis Tselekidis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9aqrxbsvjh7f0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05429",
  "fulltext_url": null,
  "id": "9aqrxbsvjh7f0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05429",
  "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.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05429",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9aqrxbsvjh7f0.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05429",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05429"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Logarithmically Slim Polygons",
  "title_text": "Logarithmically Slim Polygons",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/9aqrxbsvjh7f0",
  "venue": "arXiv",
  "versions": []
}