{
  "abstract": "Let $M$ be a complete Kähler manifold of complex dimension $n\\geq 1$ whose Kähler form is $d$-bounded in the sense of Gromov. We prove that its Bergman space, namely the Hilbert space of $L^2$ holomorphic $n$-forms, is infinite-dimensional. The proof combines Gromov's construction of auxiliary holomorphic line bundles, parameter-uniform $\\db$ estimates, and $L^2$ methods with singular weights.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05205",
  "author_total": 2,
  "authors": [
    {
      "name": "Bo-Yong Chen"
    },
    {
      "name": "Jujie Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ah9g46xcyz80b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05205",
  "fulltext_url": null,
  "id": "ah9g46xcyz80b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05205",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7220649624",
  "pdf_url": "https://arxiv.org/pdf/2610.05205",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ah9g46xcyz80b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05205",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05205"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Infinite-Dimensionality of Bergman Spaces on\\ Complete $d$-Bounded Kähler Manifolds",
  "title_text": "Infinite-Dimensionality of Bergman Spaces on\\ Complete d-Bounded Kähler Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ah9g46xcyz80b",
  "venue": "arXiv",
  "versions": []
}