{
  "abstract": "We prove Cohn--Vossen-type scalar curvature inequalities on complete noncompact Riemannian manifolds with nonnegative Ricci curvature, motivated by Yau's higher-dimensional problem. For $n\\ge3$, we obtain an $O(r^{n-2})$ normalized growth estimate under a $\\mathbb Z^{n-2}$ subgroup condition on $π_1(M)$. For locally conformally flat manifolds, we prove the corresponding normalized estimate in the non-$\\mathbb R^n$ case and derive polynomial or exponential upper bounds in the conformally Euclidean case. In dimension three, we prove the sharp asymptotic scalar-curvature flux estimate $8π$ under quadratic scalar-curvature decay, confirming the Munteanu--Wang conjectural $8π$ bound in this setting; we also prove finiteness of the flux for manifolds with a foliated end. Finally, under the Cohn--Vossen-scale scalar-growth hypothesis, we prove weighted analogues for the weighted scalar curvature $\\mathrm{Sc}_{α,β}$ on weighted Riemannian manifolds with nonnegative Bakry--Émery Ricci curvature, including sharp distinctions between the finite-dimensional and infinite-dimensional Bakry--Émery regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.01368",
  "author_total": 1,
  "authors": [
    {
      "name": "Jialong Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/espn5k9c4d20b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.01368",
  "fulltext_url": null,
  "id": "espn5k9c4d20b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.01368",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7163125238",
  "pdf_url": "https://arxiv.org/pdf/2606.01368",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/espn5k9c4d20b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2606.01368",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.01368"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Cohn--Vossen-Type Inequalities for Three-Manifolds and Locally Conformally Flat Manifolds",
  "title_text": "Cohn--Vossen-Type Inequalities for Three-Manifolds and Locally Conformally Flat Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/espn5k9c4d20b",
  "venue": "arXiv",
  "versions": []
}