{
  "abstract": "We address Problems~2.2(i), 2.2(ii), and~2.4 in Dinh--Sibony's list. For a saturated holomorphic curve foliation on a compact Kähler manifold with finitely many singularities, every positive directed $dd^c$-closed current has finite Poincaré mass. Thus linearizability is not needed for the geometric ergodic theorem in this setting. We construct a projective surface with dense hyperbolic leaves and a diffuse extremal current whose Nevanlinna averages converge at a uniform reciprocal logarithmic rate. This is an existence result for a chosen foliation, not a rate theorem for an arbitrary prescribed foliation. Under the hypotheses of the first result, every hyperbolic leaf has a logarithmic lower bound for its Nevanlinna characteristic, even if no diffuse directed current exists. Positive-dimensional singular sets are not treated.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00228",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhangchi Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3b9ch6dz037yg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00228",
  "fulltext_url": null,
  "id": "3b9ch6dz037yg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00228",
  "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.CV"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7216492850",
  "pdf_url": "https://arxiv.org/pdf/2610.00228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3b9ch6dz037yg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Answers to three problems in Dinh-Sibony's list on holomorphic foliation theory",
  "title_text": "Answers to three problems in Dinh-Sibony's list on holomorphic foliation theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/3b9ch6dz037yg",
  "venue": "arXiv",
  "versions": []
}