{
  "abstract": "If $T$ is an optimal transport map between bounded convex domains $Ω$ and $Ω'$, we characterize the regularity/singularity dichotomy for $DT$ at $(x,T(x)) \\in \\partial Ω\\times \\partial Ω'$. This is obtained through a new approach to the regularity theory based on affine degenerations of the tangent cones to $(Ω, Ω')$ at $(x,T(x))$. We formulate a general principle relating the optimal boundary regularity to a stability criterion and an $\\mathrm{SL}(n)$ moduli space of pairs of convex cones. Among other results, we establish geometric criteria for existence and non-existence of homogeneous optimal transport maps between convex cones.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37847",
  "author_total": 3,
  "authors": [
    {
      "name": "Tristan C. Collins"
    },
    {
      "name": "Benjy Firester"
    },
    {
      "name": "Freid Tong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crejf515pmf99.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37847",
  "fulltext_url": null,
  "id": "crejf515pmf99",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37847",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214976620",
  "pdf_url": "https://arxiv.org/pdf/2609.37847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crejf515pmf99.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Optimal regularity of optimal transport and degenerations of convex cones",
  "title_text": "Optimal regularity of optimal transport and degenerations of convex cones",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/crejf515pmf99",
  "venue": "arXiv",
  "versions": []
}