{
  "abstract": "We prove that, for every positive integer $r$, the positive normalized diameters of isometric quotients of simply connected irreducible compact Riemannian symmetric spaces of rank $r$ have a uniform positive lower bound. The bound is independent of the dimension and of the acting group, which need not be connected. For the higher-dimensional Grassmannian families, we obtain an explicit bound for positive-dimensional acting groups by constructing nonconstant invariant functions of bounded trigonometric degree. The real and complex cases use moment maps. The quaternionic case follows from a quartic rigidity theorem proved by means of invariant four-forms and the classification of compact quaternionic symmetric spaces. We also give examples showing why the rank and the relative scales of product factors must be controlled.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21535",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiqi Chen"
    },
    {
      "name": "Shaoqiang Deng"
    },
    {
      "name": "Hui Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1jk4sy7x65v4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21535",
  "fulltext_url": null,
  "id": "d1jk4sy7x65v4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21535",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213948906",
  "pdf_url": "https://arxiv.org/pdf/2609.21535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1jk4sy7x65v4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.21535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A diameter gap for irreducible compact symmetric spaces of fixed rank",
  "title_text": "A diameter gap for irreducible compact symmetric spaces of fixed rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/d1jk4sy7x65v4",
  "venue": "arXiv",
  "versions": []
}