{
  "abstract": "We study complete stable minimal hypersurfaces in Riemannian manifolds under various curvature assumptions. In an $(n+1)$-dimensional complete oriented manifold with nonnegative scalar curvature, we prove that no complete oriented noncompact stable minimal hypersurface can be conformally equivalent to a bounded domain in an $n$-dimensional manifold with nonpositive scalar curvature. As a consequence, there exists no complete stable minimal hypersurface in $\\mathbb{R}^{n+1}$ that is conformally equivalent to a bounded domain in $\\mathbb{R}^n$. We also show that compact stable minimal hypersurfaces in manifolds with nonnegative scalar curvature have nonnegative smooth Yamabe invariant and we characterize the equality case. Next, we consider complete two-sided stable minimal hypersurfaces in ambient manifolds with pinched sectional curvature. Under an additional curvature condition that makes the second fundamental form a Codazzi tensor, we obtain a rigidity result under an $L^2$-condition on the second fundamental form and derive an upper bound for the first eigenvalue of the Laplacian. Finally, we establish that any complete noncompact two-sided minimal hypersurface immersed in a warped product manifold is stable, provided that the angle function is positive and the second derivative of the warping function is nonnegative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. Geom. Anal. 36, 351 (2026)",
  "arxiv": "2609.17078",
  "author_total": 2,
  "authors": [
    {
      "name": "Jooyeon Park"
    },
    {
      "name": "Keomkyo Seo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aavgzm1hcnpyz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17078",
  "fulltext_url": null,
  "id": "aavgzm1hcnpyz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17078",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.17078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aavgzm1hcnpyz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Conformal structures and rigidity of complete stable minimal hypersurfaces",
  "title_text": "Conformal structures and rigidity of complete stable minimal hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/aavgzm1hcnpyz",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s12220-026-02604-9",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}