{
  "abstract": "We prove Gromov's hyperbolic hyperspherical radius comparison and rigidity conjectures in all dimensions $n\\ge3$, without the spin assumption. Let $(X^n, g)$ be a smooth, oriented, connected, compact Riemannian manifold with nonempty smooth connected boundary $S$. If ${\\rm Sc}_g\\ge -n(n-1)$ and $H_S\\ge (n-1)\\coth R$ for some $R>0$, then ${\\rm Rad}(S,g_S)\\le\\sinh R$, with equality if and only if $(X^n,g)$ is isometric to the closed hyperbolic geodesic ball of radius $R$. Under the same curvature bounds, every smooth $1$-Lipschitz map of nonzero degree from $S$ to the boundary of the hyperbolic geodesic ball of radius $R$ extends to an isometry of the fillings. Here, $g_S$ is the induced boundary metric, $H_S$ is the mean curvature of $S$ with respect to the outward unit normal, and ${\\rm Rad}(S,g_S)$ denotes the hyperspherical radius.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28450",
  "author_total": 2,
  "authors": [
    {
      "name": "Xumin Jiang"
    },
    {
      "name": "Zhehui Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05kcdvabchdbg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28450",
  "fulltext_url": null,
  "id": "05kcdvabchdbg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28450",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223140861",
  "pdf_url": "https://arxiv.org/pdf/2610.28450",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05kcdvabchdbg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28450",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28450"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hyperbolic comparison and rigidity for the hyperspherical radius",
  "title_text": "Hyperbolic comparison and rigidity for the hyperspherical radius",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/05kcdvabchdbg",
  "venue": "arXiv",
  "versions": []
}