{
  "abstract": "We prove that every entire smooth strictly plurisubharmonic solution of the self-shrinking $J$-equation on $\\mathbb{C}^n$ is a quadratic polynomial. This removes the asymptotic lower bound assumption on the complex Hessian in \\cite[Theorem 4]{HJ}. The result also recovers the corresponding real rigidity theorem in \\cite[Theorem 1.1]{HOW} as a special case. More generally, our method applies to self-shrinking equations associated with a broad class of fully nonlinear elliptic operators satisfying suitable structural conditions, including the adjacent inverse complex Hessian quotient operators $-σ_{k-1}/σ_{k}$, $1\\leq k\\leq n$. For the remaining quotients $-σ_l/σ_k$ with $l<k-1$, we prove the same rigidity conclusion under the additional assumption that the solution is proper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29546",
  "author_total": 2,
  "authors": [
    {
      "name": "Yiyang Pan"
    },
    {
      "name": "Wenlong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4g5s3j4a5pn59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29546",
  "fulltext_url": null,
  "id": "4g5s3j4a5pn59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29546",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7166739121",
  "pdf_url": "https://arxiv.org/pdf/2606.29546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g5s3j4a5pn59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2606.29546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Bernstein Theorem for the Self-Shrinking $J$-Equation and Some Generalizations",
  "title_text": "A Bernstein Theorem for the Self-Shrinking J-Equation and Some Generalizations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4g5s3j4a5pn59",
  "venue": "arXiv",
  "versions": []
}