{
  "abstract": "Let $Ω\\subset\\mathbb C^n$, $n\\ge2$, be a bounded connected pseudoconvex domain whose boundary contains a smooth strongly pseudoconvex point. We prove that if the Bergman metric of $Ω$ is extremal, then its scalar curvature is identically $-n$, and that constant scalar curvature forces the Bergman metric to be Kähler--Einstein. Consequently, extremality, constant scalar curvature, and the Kähler--Einstein condition are equivalent in this setting. A key analytic ingredient is a local unique-continuation theorem for the Bergman Laplacian at an ACH boundary, proved using Hörmander's Carleman estimate. We also obtain an extension for possibly unbounded pseudoconvex domains: if the Bergman metric is cscK or extremal near such a boundary point, then it is well-defined and Kähler--Einstein throughout the locus where $K_Ω(z,z)>0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04590",
  "author_total": 2,
  "authors": [
    {
      "name": "Peter Ebenfelt"
    },
    {
      "name": "Soumya Ganguly"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8czz5wpfjb7xz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04590",
  "fulltext_url": null,
  "id": "8czz5wpfjb7xz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04590",
  "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": "W7220677013",
  "pdf_url": "https://arxiv.org/pdf/2610.04590",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8czz5wpfjb7xz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04590",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04590"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Rigidity of Extremal and cscK Bergman Metrics on Pseudoconvex Domains",
  "title_text": "Rigidity of Extremal and cscK Bergman Metrics on Pseudoconvex Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8czz5wpfjb7xz",
  "venue": "arXiv",
  "versions": []
}