{
  "abstract": "Considering an $n$-dimensional compact Riemannian manifold with a boundary that satisfies a Serrin-type problem, we prove sharp upper and lower bounds for the area of such a boundary. Then, we present the main result of this paper: a divergence formula for a special vector field on a given Riemannian manifold. This divergence formula is closely related to sub-static manifolds and related metrics, e.g., $V$-static, static, and electrostatic manifolds. We show Minkowski-type inequalities for $V$-sub-static manifolds under different Neumann boundary conditions. Moreover, we prove an area-charge inequality for compact (and noncompact) electrostatic manifolds. The main application of the divergence formula presented in this work generalizes the classical result of Boucher--Gibbons--Horowitz: we prove that an asymptotically hyperbolic space of a static spacetime satisfying the null convergence condition must be the hyperbolic space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23184",
  "author_total": 3,
  "authors": [
    {
      "name": "Benedito Leandro"
    },
    {
      "name": "Ilton Menezes"
    },
    {
      "name": "Rafael Novais"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zn9fmakwhd0m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23184",
  "fulltext_url": null,
  "id": "8zn9fmakwhd0m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23184",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7204190950",
  "pdf_url": "https://arxiv.org/pdf/2608.23184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zn9fmakwhd0m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2608.23184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Semilinear overdetermined problems, a divergence formula, and geometric inequalities",
  "title_text": "Semilinear overdetermined problems, a divergence formula, and geometric inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/8zn9fmakwhd0m",
  "venue": "arXiv",
  "versions": []
}