{
  "abstract": "We construct a smooth embedded annulus in Euclidean 3-space with negative Gauss curvature in its interior whose boundary consists of strictly convex curves in planes tangent to the annulus, and which contains closed asymptotic curves. This gives a counterexample to a 1962 conjecture of Nirenberg. The construction is based on Lelieuvre's formula, which yields a closed curve that is then realized as an asymptotic curve on a ruled annulus. The second asymptotic curve is obtained from a periodic solution of a Riccati equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13848",
  "author_total": 4,
  "authors": [
    {
      "name": "Harrison Banks"
    },
    {
      "name": "Mohammad Ghomi"
    },
    {
      "name": "Hongda Qiu"
    },
    {
      "name": "Matteo Raffaelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hyhfjwh3t676.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13848",
  "fulltext_url": null,
  "id": "5hyhfjwh3t676",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13848",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7221521292",
  "pdf_url": "https://arxiv.org/pdf/2610.13848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hyhfjwh3t676.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.13848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13848"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A counterexample to Nirenberg's conjecture on closed asymptotic curves",
  "title_text": "A counterexample to Nirenberg's conjecture on closed asymptotic curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/5hyhfjwh3t676",
  "venue": "arXiv",
  "versions": []
}