{
  "abstract": "We establish a new local-to-global rigidity phenomenon for the Bergman metric. Namely, under natural geometric hypotheses, a local conformal identification of Bergman metrics determines the underlying complex manifold globally, up to the unavoidable ambiguity of removing Bergman-negligible subsets. More precisely, let $Ω\\subseteq\\mathbb{C}^n$ be a bounded domain with a complete Bergman metric, and suppose that the Bergman metric of a complex manifold $M$ is locally conformal, via a holomorphic map $f$, to that of $Ω$, with a constant conformal factor when $n=1$. We prove that the given local map $f$ extends to a biholomorphism $F\\colon M\\to D$ onto a subdomain $D\\subseteqΩ$ in two complementary settings. If $M$ is Stein, then $Ω\\setminus D$ is a closed pluripolar set. If $M$ is a bounded domain and $Ω$ satisfies a natural symmetry condition expressed in terms of its automorphism orbits, then $Ω\\setminus D$ is Bergman-negligible. In particular, this applies when $Ω$ is a bounded homogeneous domain and yields a characterization, up to Bergman-negligible sets, of a class of bounded domains with locally symmetric Bergman metrics, addressing a question raised by Loi--Palmieri and Zimmer. A key ingredient in the proofs is a new Calabi-type extension theorem tailored to Bergman metrics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15998",
  "author_total": 3,
  "authors": [
    {
      "name": "Peter Ebenfelt"
    },
    {
      "name": "John N. Treuer"
    },
    {
      "name": "Ming Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8ht2zhf4c59c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15998",
  "fulltext_url": null,
  "id": "c8ht2zhf4c59c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15998",
  "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": "W7203721390",
  "pdf_url": "https://arxiv.org/pdf/2608.15998",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8ht2zhf4c59c.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2608.15998",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15998"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A new strong rigidity phenomenon for the Bergman metric",
  "title_text": "A new strong rigidity phenomenon for the Bergman metric",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/c8ht2zhf4c59c",
  "venue": "arXiv",
  "versions": []
}