{
  "abstract": "We study optimal transport with a non-convex polyhedral target in $\\mathbb{R}^n$. The closure of the singular set is locally a smooth hypersurface outside a relatively closed set of Hausdorff dimension at most $n-2$. For partial transport between domains separated by a hyperplane, the source free boundary has the same regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18756",
  "author_total": 5,
  "authors": [
    {
      "name": "Shibing Chen"
    },
    {
      "name": "Qi-Rui Li"
    },
    {
      "name": "Yuanyuan Li"
    },
    {
      "name": "Jiakun Liu"
    },
    {
      "name": "Xiaotian Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vaextkn41g7w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18756",
  "fulltext_url": null,
  "id": "4vaextkn41g7w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18756",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221817596",
  "pdf_url": "https://arxiv.org/pdf/2610.18756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vaextkn41g7w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Optimal transport to non-convex polyhedral domains",
  "title_text": "Optimal transport to non-convex polyhedral domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/4vaextkn41g7w",
  "venue": "arXiv",
  "versions": []
}