{
  "abstract": "We establish sharp Beckner--Onofri on the CR sphere $\\mathbb{S}^{2N-1}\\subset\\mathbb C^N$, $N\\ge2$, under vanishing holomorphic moments through degree $m\\ge1$. The optimal coefficients are $\\frac{1}{m+1}$. The function inequality admits a stronger form involving only the energy above degree $m$. We also prove a quantitative concentration estimate in the $1$-Wasserstein distance and show that every maximizing sequence has diverging energy and approaches the family of uniform measures on regular $(m+1)$-polygons. The proof combines subcritical minimization with rigidity of the constrained Euler--Lagrange equation, obtained from an exact radial energy identity and a Hardy space projection estimate. Finally, weighted ball automorphisms yield sharp inequalities without moment constraints, with scalar conformal, barycenter, and holomorphic Gram determinant corrections.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31092",
  "author_total": 2,
  "authors": [
    {
      "name": "Tuoxin Li"
    },
    {
      "name": "Jingxuan Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxndftkr7zp9d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31092",
  "fulltext_url": null,
  "id": "fxndftkr7zp9d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31092",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223395867",
  "pdf_url": "https://arxiv.org/pdf/2610.31092",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxndftkr7zp9d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31092",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31092"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints",
  "title_text": "Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/fxndftkr7zp9d",
  "venue": "arXiv",
  "versions": []
}