{
  "abstract": "In this paper we study a class of 1-homogeneous solutions of the one-phase problem coming from the Cartan isoparametric cubic polynomials, which exist only in dimensions $d=5,8,14,26$. Our main result shows that they are unstable in dimensions $d=5,8,14$, and minimizing in dimension $d=26$. This provides the first example of a singular minimizing cone in the Alt-Caffarelli problem that is neither axially symmetric nor of Lawson-type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35179",
  "author_total": 2,
  "authors": [
    {
      "name": "Matteo Carducci"
    },
    {
      "name": "Bozhidar Velichkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/192dvw78tdgjq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35179",
  "fulltext_url": null,
  "id": "192dvw78tdgjq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35179",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214776959",
  "pdf_url": "https://arxiv.org/pdf/2609.35179",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/192dvw78tdgjq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35179",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35179"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem",
  "title_text": "A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/192dvw78tdgjq",
  "venue": "arXiv",
  "versions": []
}