{
  "abstract": "Let $4\\le n\\le7$ and let $(M^n,g)$ be a complete, connected, orientable, noncompact Riemannian manifold of positive scalar curvature. We prove that if the asymptotic quadratic scalar curvature coefficient of $g$ is greater than $(n-1)/n$, then $M$ carries a complete smooth metric whose scalar curvature is at least one. The threshold $(n-1)/n$ and the strict inequality are optimal. This confirms the second part of Gromov's critical rate of decay conjecture in dimensions four through seven.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03676",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhehui Wang"
    },
    {
      "name": "Jintian Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bddvxtgxchx3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03676",
  "fulltext_url": null,
  "id": "6bddvxtgxchx3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03676",
  "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": "W7208752517",
  "pdf_url": "https://arxiv.org/pdf/2609.03676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bddvxtgxchx3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.03676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03676"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quadratic Scalar Curvature Decay and Uniform Positivity in Dimensions Four through Seven",
  "title_text": "Quadratic Scalar Curvature Decay and Uniform Positivity in Dimensions Four through Seven",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/6bddvxtgxchx3",
  "venue": "arXiv",
  "versions": []
}