{
  "abstract": "Let $k\\in\\mathbb N$ satisfy $1<k<n/2$, and let $Σ^p\\subset\\Sn^n$ be a closed smooth embedded submanifold. We prove that a complete conformal metric $g=v^{-2}g_{\\Sn^n}$ on $\\Sn^n\\setminusΣ$ satisfying $λ(g^{-1}A_g)\\in\\Gk$ and $σ_k(g^{-1}A_g)=κ>0$ must obey \\[ p\\leq p_k(n), \\] where $p_k$ is the model threshold determined by $\\Hh^{p+1}\\times\\Sn^{n-p-1}$. When $k=2$ and $n=m^2$, we construct a smooth complete equality example on $\\Sn^n\\setminus\\Sn^{(m^2-m-2)/2}$. We also prove that the strict inequality $p<p_k(n)$ holds under a finite positive linear-contact hypothesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.16571",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiahuan Li"
    },
    {
      "name": "Yilu Liu"
    },
    {
      "name": "Xi-Nan Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mt8wey2kn69a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.16571",
  "fulltext_url": null,
  "id": "1mt8wey2kn69a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.16571",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7203682916",
  "pdf_url": "https://arxiv.org/pdf/2608.16571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mt8wey2kn69a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.16571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.16571"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Model-threshold Dimension Bound and Sharp Critical Ends for Smooth Singular Sets of Constant Positive $σ_k$-curvature Metrics",
  "title_text": "A Model-threshold Dimension Bound and Sharp Critical Ends for Smooth Singular Sets of Constant Positive σ_k-curvature Metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1mt8wey2kn69a",
  "venue": "arXiv",
  "versions": []
}