{
  "abstract": "This paper relates the minimal Harder--Narasimhan slope to the surjectivity of real-linear Cauchy--Riemann operators. We establish a conformally invariant $L^2$ criterion and an asymptotic slope criterion, which yield higher-rank automatic transversality criteria for pseudoholomorphic curves beyond the classical rank-one framework. Applications to pseudoholomorphic spheres in $S^6$ provide quantitative $L^2$ obstructions to the integrability of almost complex structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18997",
  "author_total": 2,
  "authors": [
    {
      "name": "Qingchun Ji"
    },
    {
      "name": "Jun Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eexeqcs7b4nm8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18997",
  "fulltext_url": null,
  "id": "eexeqcs7b4nm8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18997",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7203862090",
  "pdf_url": "https://arxiv.org/pdf/2608.18997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eexeqcs7b4nm8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.18997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18997"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Surjectivity of real-linear Cauchy--Riemann operators: from the minimal Harder--Narasimhan slope to automatic transversality",
  "title_text": "Surjectivity of real-linear Cauchy--Riemann operators: from the minimal Harder--Narasimhan slope to automatic transversality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/eexeqcs7b4nm8",
  "venue": "arXiv",
  "versions": []
}