{
  "abstract": "For every integer $m\\geq 3$, we construct a smooth Riemannian metric $g$ on a manifold diffeomorphic to $S^m$ such that $\\text{sec}_g\\geq 0$, every sectional curvature is strictly positive away from a closed nowhere-dense set, and the point locus on which some sectional curvature vanishes has Hausdorff dimension exactly $\\frac{1}{2}$. The metric is induced on the boundary of a smooth convex body in $\\mathbb{R}^{m+1}$. The essential local model is a convex graph whose Hessian has a one-dimensional kernel precisely on a Cantor subset of one coordinate axis; a regularized maximum then inserts this graph into a round sphere without introducing additional degenerate points. The main content of this paper is generated by ChatGPT 5.6 and verified by the author.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27898",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuhang Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01hjkjhqqx1vg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27898",
  "fulltext_url": null,
  "id": "01hjkjhqqx1vg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27898",
  "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": "W7214205154",
  "pdf_url": "https://arxiv.org/pdf/2609.27898",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01hjkjhqqx1vg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27898",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27898"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Smooth Nonnegatively Curved Sphere Whose Zero-Curvature Point Locus Has Hausdorff Dimension 1/2",
  "title_text": "A Smooth Nonnegatively Curved Sphere Whose Zero-Curvature Point Locus Has Hausdorff Dimension 1/2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/01hjkjhqqx1vg",
  "venue": "arXiv",
  "versions": []
}