{
  "abstract": "Let $B(δ)\\subset\\mathbb S^n$ be a geodesic ball with the round metric $\\bar{g}$ of sectional curvature one, where $n\\geq3$ and $0<δ<π/2$. We prove local scalar-curvature rigidity under preservation of the induced boundary metric and a one-sided lower bound for the boundary mean curvature. More precisely, every sufficiently small $C^{2,α}$ perturbation $g$ of $\\bar{g}$ satisfying $R(g)\\geq n(n-1)$ and $H(g)\\geq(n-1)\\cotδ$ is round up to a diffeomorphism fixing the boundary pointwise. Inspired by the scalar--vector--tensor decomposition used in the study of Yamabe compactness, we establish positivity of the Brendle--Marques quadratic form in the divergence-free gauge for variations preserving the induced boundary metric and satisfying the joint linearized constraints $D R_{\\bar{g}}(h)=D H_{\\bar{g}}(h)=0$. The hemisphere counterexamples of Brendle--Marques--Neves show that the radius range is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29579",
  "author_total": 2,
  "authors": [
    {
      "name": "Liuwei Gong"
    },
    {
      "name": "Juncheng Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70jwhy4k5y8z3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29579",
  "fulltext_url": null,
  "id": "70jwhy4k5y8z3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29579",
  "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": "W7223200594",
  "pdf_url": "https://arxiv.org/pdf/2610.29579",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70jwhy4k5y8z3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29579"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sharp local scalar-curvature rigidity of spherical caps",
  "title_text": "Sharp local scalar-curvature rigidity of spherical caps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/70jwhy4k5y8z3",
  "venue": "arXiv",
  "versions": []
}