{
  "abstract": "In this note, using J.-P. Demailly's $L^2$ existence theorem for possibly incomplete Kähler metrics, we establish $L^2$ estimates and vanishing theorems for a class of domains in $\\mathbb P^n$ without any boundary regularity assumptions. In particular, we give an affirmative answer to M.-C. Shaw's question concerning the vanishing of the $L^2$ Dolbeault cohomology groups of projective Hartogs triangles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37572",
  "author_total": 1,
  "authors": [
    {
      "name": "Jian Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fsfc7vcpm549a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37572",
  "fulltext_url": null,
  "id": "fsfc7vcpm549a",
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  "landing_url": "https://arxiv.org/abs/2610.37572",
  "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": "W7224118376",
  "pdf_url": "https://arxiv.org/pdf/2610.37572",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fsfc7vcpm549a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37572",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37572"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Vanishing theorems for $L^2$ Dolbeault cohomology groups of projective Hartogs triangles",
  "title_text": "Vanishing theorems for L^2 Dolbeault cohomology groups of projective Hartogs triangles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fsfc7vcpm549a",
  "venue": "arXiv",
  "versions": []
}