{
  "abstract": "We construct smooth closed embedded minimal surfaces with everywhere negative Gaussian curvature in the unit round four-sphere. More precisely, for every sufficiently large integer $m$, our construction gives a minimal surface $Σ_m$ of genus $m^2+1$ such that $\\operatorname{Area}(Σ_m)\\to 4π^2$ as $m\\to+\\infty$. This result yields a complete solution to Problem 101 in Yau's 1982 list of open problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12238",
  "author_total": 1,
  "authors": [
    {
      "name": "Riccardo Caniato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0y9554b2pqx6e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12238",
  "fulltext_url": null,
  "id": "0y9554b2pqx6e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12238",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221184945",
  "pdf_url": "https://arxiv.org/pdf/2610.12238",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0y9554b2pqx6e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12238",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12238"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Negatively Curved Minimal Surfaces in the Round Four-Sphere",
  "title_text": "Negatively Curved Minimal Surfaces in the Round Four-Sphere",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0y9554b2pqx6e",
  "venue": "arXiv",
  "versions": []
}