{
  "abstract": "Let $(M^{n}, g)$ be a complete, simply connected Riemannian manifold without boundary, of dimension $n\\ge3$, with curvature operator at least that of the unit sphere. We prove that $$\\int_M {\\rm scal}(x)\\ d {\\rm Vol}_x\\le n(n-1)ω_n,$$ where $ω_n$ is the volume of the unit $n$-sphere. Equality holds if and only if $(M,g)$ is isometric to the unit round sphere. In fact, we obtain a stronger bound containing ${\\rm Vol}(M, g)$. In even dimensions, the proof follows from the Chern-Gauss-Bonnet formula. In odd dimensions, we apply the corresponding boundary formula to Deruelle's Ricci expander filling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19851",
  "author_total": 3,
  "authors": [
    {
      "name": "Jian Ge"
    },
    {
      "name": "Chuanhuan Li"
    },
    {
      "name": "Ronggang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f358wzdd98bf6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19851",
  "fulltext_url": null,
  "id": "f358wzdd98bf6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19851",
  "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": "W7213579542",
  "pdf_url": "https://arxiv.org/pdf/2609.19851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f358wzdd98bf6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Total scalar curvature under a curvature operator lower bound",
  "title_text": "Total scalar curvature under a curvature operator lower bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/f358wzdd98bf6",
  "venue": "arXiv",
  "versions": []
}