{
  "abstract": "We prove that the cone $C(Σ)$ in $\\mathbb R^4$ over a suitable minimal Möbius band $Σ\\subset \\mathbb S^3$ is locally mass-minimising with coefficients in $\\mathbb Z_2$. This proves a conjecture by Brian White in the context of models of boundary singularities of Plateau's problem in ambient dimension $4$ or higher. The key insight is that the cylindrical slices $C(Σ)\\cap \\{(z,w)\\in \\mathbb R^2 \\times \\mathbb R^2 : |w|=r\\}$ are minimal surfaces in a flat rank-one translation quotient of $\\mathbb R^3$. In fact, they correspond to non-orientable minimising helicoids previously studied by Antonio Ros. We also show that, up to rigid motions, the minimising cones $C(Σ)\\times \\mathbb R^{n-4}\\subset \\mathbb R^n$ are the only non-planar minimal hypercones with boundary $\\mathbb R^{n-2}$ which are smooth away from the boundary that satisfy the minimal cylindrical slice property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24909",
  "author_total": 2,
  "authors": [
    {
      "name": "Marco A. M. Guaraco"
    },
    {
      "name": "Davide Parise"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7e26h3w98pthn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24909",
  "fulltext_url": null,
  "id": "7e26h3w98pthn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24909",
  "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": "W7214013455",
  "pdf_url": "https://arxiv.org/pdf/2609.24909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7e26h3w98pthn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "White's cone over the Möbius band is area-minimising",
  "title_text": "White's cone over the Möbius band is area-minimising",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/7e26h3w98pthn",
  "venue": "arXiv",
  "versions": []
}