{
  "abstract": "In this paper, we prove several results concerning the function theory of complete Hermitian manifolds with vanishing Chern curvature, which we refer to as complete Chern-flat manifolds. First, we show that any complete simply connected Chern-flat manifold is elliptic in the sense of Gromov. Moreover, it is biholomorphic to a complex Lie group if the torsion has polynomial growth. We also construct examples of complete Chern-flat manifolds with torsion of exponential growth, but the underlying complex manifolds do not admit any complex Lie group structures. Next, we obtain sharp upper bounds on the dimensions of holomorphic functions of polynomial growth on complete Chern-flat manifolds, without any growth assumption on the torsion. Finally, we prove that any complete Chern-flat manifold admitting polynomial-growth holomorphic functions that form a local holomorphic coordinate system at some point is biholomorphic to complex Euclidean space. These results generalize our previous work, where we assume that the torsion has sublinear growth. Our approach combines Cauchy estimates with nilpotent analysis along the orbits of holomorphic flows generated by parallel unitary frames on such manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10159",
  "author_total": 3,
  "authors": [
    {
      "name": "Duoxin Li"
    },
    {
      "name": "Hanyu Wu"
    },
    {
      "name": "Bo Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9vvpz9ed6ajrp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10159",
  "fulltext_url": null,
  "id": "9vvpz9ed6ajrp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10159",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.10159",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vvpz9ed6ajrp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10159",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10159"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Holomorphic functions on complete Hermitian manifolds with flat Chern connection, II",
  "title_text": "Holomorphic functions on complete Hermitian manifolds with flat Chern connection, II",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:25Z",
  "url": "https://research.draconitic.com/paper/9vvpz9ed6ajrp",
  "venue": "arXiv",
  "versions": []
}