{
  "abstract": "We give counterexamples to Yau's question on normalized scalar curvature integrals in every dimension $n\\geq4$. For each such $n$, there exists a smooth complete Riemannian metric $g$ on $\\mathbb{R}^n$ with nonnegative Ricci curvature and a pole such that \\[ \\lim_{R\\to\\infty}R^{2-n}\\int_{B_q(R)}\\mathrm{Scal}_g\\,\\mathrm dV_g=+\\infty \\] for every fixed $q\\in\\mathbb{R}^n$. Here $B_q(R)$ denotes the geodesic ball of radius $R$ centered at $q$, and $\\mathrm{Scal}_g$ is the scalar curvature of $g$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10323",
  "author_total": 1,
  "authors": [
    {
      "name": "Haoxuan Cheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38c2dq7226qwf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10323",
  "fulltext_url": null,
  "id": "38c2dq7226qwf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10323",
  "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": "W7212168931",
  "pdf_url": "https://arxiv.org/pdf/2609.10323",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38c2dq7226qwf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10323",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10323"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Unbounded normalized scalar curvature integrals in dimension four",
  "title_text": "Unbounded normalized scalar curvature integrals in dimension four",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/38c2dq7226qwf",
  "venue": "arXiv",
  "versions": []
}