{
  "abstract": "We study scalar curvature integrals over geodesic balls on complete noncompact manifolds. Under nonnegative Ricci curvature and rotational symmetry, we prove the sharp bound \\[ \\int_{B_p(r)}S\\text{d}μ_g \\le 2n(n-1)ω_n \\bigl(1-v^{1/(n-1)}\\bigr)r^{n-2}, \\] when $p$ is the rotational origin. Here $ω_n$ is the volume of the Euclidean unit ball and $v=V_{M^n}$ is the asymptotic volume ratio. In dimension three, with the center at a pole, we obtain a sharp bound \\[ \\int_{B_p(r)}S\\text{d}μ_g\\le16πr, \\] without any positive volume growth assumption. We also obtain a bound for every asymptotic volume ratio which is sharp for $0\\le v\\le1/4$. Under nonnegative sectional curvature and $v>0$, we prove the explicit bound at arbitrary centers \\[ \\int_{B_p(r)}S\\text{d}μ_g\\le12π(1-v)v^{-3}r. \\] If $0\\le1-v\\le1/100$, we further obtain \\[ \\int_{B_p(r)}S\\text{d}μ_g\\le\\bigl[8π(1-v)+200π(1-v)^2\\bigr]r. \\] The leading coefficient $8π$ is sharp, and a remainder of quadratic order in $1-v$ is necessary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29596",
  "author_total": 1,
  "authors": [
    {
      "name": "Qixuan Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8y97aw417ksmq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29596",
  "fulltext_url": null,
  "id": "8y97aw417ksmq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29596",
  "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": "W7223217828",
  "pdf_url": "https://arxiv.org/pdf/2610.29596",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8y97aw417ksmq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29596",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29596"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Scalar curvature integrals on geodesic balls",
  "title_text": "Scalar curvature integrals on geodesic balls",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/8y97aw417ksmq",
  "venue": "arXiv",
  "versions": []
}