{
  "abstract": "We classify the homotheties of the complete Cheng--Yau Kähler--Einstein metrics on the two-dimensional Thullen domains $M(μ)$, $μ>0$, that admit Kähler immersions into $\\mathbb{CH}^{\\infty}$. With $\\Ric(g_{\\mathrm{CY}})=-3g_{\\mathrm{CY}}$, an immersion of $c\\,g_{\\mathrm{CY}}$ exists exactly when $0<μ\\leqμ_+$ and $0<c\\leq3\\min\\{1,μ\\}/(μ+2)$. The critical parameter $μ_+>1$ is characterized by an explicit equation, and its endpoint is included. Every admissible metric has a proper global Kähler embedding. The same parameter interval classifies immersibility into flat and projective Hilbert space, where every positive homothety admits a proper global embedding. Beyond the wall, all three targets are excluded at every positive scale. The proof combines an algebraic normalization of the Cheng--Yau equation, all-order coefficient estimates, and complex continuation of a scalar flow. For $μ\\neq1$, the resulting complete nonhomogeneous examples disprove proposed Kähler--Einstein rigidity conjectures in the complex-hyperbolic and flat Hilbert settings. We also prove a complementary rigidity theorem for Bergman--Hartogs domains and construct complete $η$-Einstein Sasakian manifolds with nonhomogeneous Riemannian metrics and proper global Sasakian embeddings into the infinite-dimensional Heisenberg space form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.21911",
  "author_total": 2,
  "authors": [
    {
      "name": "Mirel Caibăr"
    },
    {
      "name": "Andrea Loi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bvx89jb4scby.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.21911",
  "fulltext_url": null,
  "id": "2bvx89jb4scby",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.21911",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7204186171",
  "pdf_url": "https://arxiv.org/pdf/2608.21911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bvx89jb4scby.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2608.21911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.21911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Complex Hyperbolic Immersions of Cheng--Yau Metrics on Thullen Domains",
  "title_text": "Complex Hyperbolic Immersions of Cheng--Yau Metrics on Thullen Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/2bvx89jb4scby",
  "venue": "arXiv",
  "versions": []
}