{
  "abstract": "We show that, in every space dimension $n\\ge2$, the singular set $Σ$ of a generic (in the Baire-category sense) solution of the Stefan problem is countably parabolically $(n-2)$-rectifiable. In particular, $\\dim_{\\mathrm{par}}(Σ)\\le n-2$. This is achieved by proving the following sharp result: in every space dimension, points of the maximal stratum of a generic solution are discrete in space-time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35780",
  "author_total": 2,
  "authors": [
    {
      "name": "Giacomo Colombo"
    },
    {
      "name": "Alessio Figalli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95854sneqpjgx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35780",
  "fulltext_url": null,
  "id": "95854sneqpjgx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35780",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223953553",
  "pdf_url": "https://arxiv.org/pdf/2610.35780",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95854sneqpjgx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.35780",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35780"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The generic structure of the singular set in the Stefan problem",
  "title_text": "The generic structure of the singular set in the Stefan problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/95854sneqpjgx",
  "venue": "arXiv",
  "versions": []
}