{
  "abstract": "We prove a boundary analogue of the rigidity theorem for Ricci-pinched three-manifolds under a superquadratic volume-growth assumption. More precisely, we show that a complete connected three-manifold with convex boundary, pinched Ricci tensor, and pinched second fundamental form is isometric to the Euclidean half-space. The proof is potential-theoretic. We construct and study mixed Dirichlet--Neumann $p$-capacitary potentials, establish monotonicity formulas for their free-boundary level sets, and use a weak Gauss--Bonnet formula adapted to this setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23261",
  "author_total": 2,
  "authors": [
    {
      "name": "Chao Xia"
    },
    {
      "name": "Jincong Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qwfy80vtgngk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23261",
  "fulltext_url": null,
  "id": "3qwfy80vtgngk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23261",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.23261",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qwfy80vtgngk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23261",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23261"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Ricci-pinched 3-Manifolds with second-fundamental-form-pinched Boundary",
  "title_text": "Ricci-pinched 3-Manifolds with second-fundamental-form-pinched Boundary",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/3qwfy80vtgngk",
  "venue": "arXiv",
  "versions": []
}