{
  "abstract": "In this paper, we prove that for every $m,n\\geq 2$, the orthogonal product $S_m\\times S_n\\subset\\R^m\\times\\R^n$ is an Almgren minimal cone of dimension $m+n-2$, where $S_k\\subset\\R^k$ is the cone over the $(k-2)$-skeleton of a regular $k$-simplex. Lawlor and Morgan \\cite{LM94} proved the minimality of each $S_k$ by paired calibrations, while Guy David \\cite{DJT, GD13} later raised the general question whether products of Almgren minimal sets remain minimal. Our theorem gives a affirmative answer to this product question within the entire Lawlor-Morgan regular-simplex family. It extends the isolated example \\(\\Y\\times \\Y\\), the product of two 1-dimensional $\\Y$ sets, proved in 2014 by the second author, simultaneously to all pairwise products \\(S_m\\times S_n\\), and therefore produces a large new family of possible codimension-two singularities for Plateau's problem. The key idea of the proof is to find a new way to combine homology with paired calibrations in higher codimension. Instead of using only the currents associated with the facets, we consider all their nonzero $\\FF$ combinations. The resulting complete family has enough algebraic symmetry to control uniformly the overlaps created by noninjective deformations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27845",
  "author_total": 3,
  "authors": [
    {
      "name": "Songsong Huang"
    },
    {
      "name": "Xiangyu Liang"
    },
    {
      "name": "Zaoyi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/041j44ph3cdnk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27845",
  "fulltext_url": null,
  "id": "041j44ph3cdnk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27845",
  "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.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.DG"
    ],
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7223099961",
  "pdf_url": "https://arxiv.org/pdf/2610.27845",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/041j44ph3cdnk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27845",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27845"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Almgren minimality of products of simplex-skeleton cones",
  "title_text": "Almgren minimality of products of simplex-skeleton cones",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/041j44ph3cdnk",
  "venue": "arXiv",
  "versions": []
}