{
  "abstract": "We prove that for all real numbers $κ,τ$ with $κ>8τ^2$ and $τ\\neq 0$, the Berger sphere $\\mathbb{E}^3(κ,τ)$ contains smooth closed embedded rotational surfaces of genus one with constant mean curvature which are contained in an open hemisphere. This disproves a conjecture of Fernández and Mira. The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol, Fable 5, and the Danus system, and then verified by the authors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23484",
  "author_total": 2,
  "authors": [
    {
      "name": "Jihao Liu"
    },
    {
      "name": "Xiang Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agn2bhsja54td.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23484",
  "fulltext_url": null,
  "id": "agn2bhsja54td",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23484",
  "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": "W7214038804",
  "pdf_url": "https://arxiv.org/pdf/2609.23484",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agn2bhsja54td.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23484",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23484"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Embedded constant mean curvature tori in hemispheres of Berger spheres",
  "title_text": "Embedded constant mean curvature tori in hemispheres of Berger spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/agn2bhsja54td",
  "venue": "arXiv",
  "versions": []
}