{
  "abstract": "In this paper, we give an alternate proof of the $ε$-regularity theorem of Wang [Comm. Cont. Math. 2003] for weakly $J$-holomorphic maps by adapting the conservation law approach of Rivière [Invent. Math. 2007]. Then we adapt the powerful quantitative stratification method of Naber--Valtorta [Ann. Math. 2017] to obtain optimal volume estimates and rectifiability for the quantitative strata of stationary $J$-holomorphic maps. In contrast with general harmonic maps, the almost complex equation gives rise to an additional symmetry improvement: Every odd-dimensional translation symmetry extends to an even-dimensional one. Consequently, consecutive even and odd strata coincide, and the $k$-th quantitative stratum satisfies a tubular-neighborhood estimate with exponent $2m-2\\lfloor k/2\\rfloor$, where $2m$ is the real dimension of the domain. The corresponding strata are $2\\lfloor k/2\\rfloor$-rectifiable, with almost-everywhere unique complex planes of symmetry. Finally, we prove that every stationary $J$-holomorphic map is smooth if the target { manifold} admits no non-constant $J$-holomorphic sphere, improving the corresponding theorem of Wang.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25813",
  "author_total": 3,
  "authors": [
    {
      "name": "Chang-Yu Guo"
    },
    {
      "name": "Ming-Lun Liu"
    },
    {
      "name": "Chang-You Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1kc61kmb48be.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25813",
  "fulltext_url": null,
  "id": "c1kc61kmb48be",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25813",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223039172",
  "pdf_url": "https://arxiv.org/pdf/2610.25813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1kc61kmb48be.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quantitative stratification and optimal regularity for stationary $J$-holomorphic maps",
  "title_text": "Quantitative stratification and optimal regularity for stationary J-holomorphic maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/c1kc61kmb48be",
  "venue": "arXiv",
  "versions": []
}