{
  "abstract": "We establish a polarized weighted Reilly identity and an exact deficit decomposition for weighted curvature integrals $I_j=\\int_ΣVE_j~\\mathrm{d}μ$ in hyperbolic space, where $V=\\cosh r$ and $E_j$ is the normalized $j$th mean curvature. For compact domains with smooth connected boundary, these yield $I_k^2\\geq I_{k-1}I_{k+1}$ under intrinsic sub-staticity at $k=1$ and static convexity with $κ\\inΓ_k\\cap\\overlineΓ_{k+1}$ for $2\\leq k\\leq n-1$, with equality precisely for geodesic balls. Under $h\\geq0$ and $Vh-V_νg\\geq0$, log-concavity and a Euclidean mixed-volume representation recover the centered-ball comparisons conjectured by Hu and Li \\cite[Conjecture~1.1]{HuLi}, allowing the weight center to lie outside the domain. Equality in these comparisons holds precisely for balls centered at the weight center.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02882",
  "author_total": 2,
  "authors": [
    {
      "name": "Shengguang Bi"
    },
    {
      "name": "Yingxiang Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cbf73wa5k6vqq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02882",
  "fulltext_url": null,
  "id": "cbf73wa5k6vqq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02882",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02882",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cbf73wa5k6vqq.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02882",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02882"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Reilly approach to weighted curvature integral inequalities in hyperbolic space",
  "title_text": "A Reilly approach to weighted curvature integral inequalities in hyperbolic space",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/cbf73wa5k6vqq",
  "venue": "arXiv",
  "versions": []
}