{
  "abstract": "We establish a parameterized Heintze--Karcher-type inequality for positive solutions of nonlinear Dirichlet problems involving the $p$-Laplacian, with $p\\geq2$, on bounded Riemannian domains. Under a Ricci curvature lower bound, positive boundary mean curvature, and suitable structural and approximation assumptions, the estimate follows from a regularized Reilly-type identity and a weighted Hessian inequality. We compare the resulting bound with previous estimates and investigate the geometry associated with equality. For $p=2$, an exact deficit identity allows the pointwise condition $f'\\leq nk$ to be replaced by a weighted integral condition. As applications, we obtain Heintze--Karcher and Soap Bubble-type rigidity results, with equality forcing the domain to be a metric ball and the solution to be radial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34252",
  "author_total": 2,
  "authors": [
    {
      "name": "Matheus Nunes Soares"
    },
    {
      "name": "Weiller F. Chaves Barboza"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3cwqnts81z22k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34252",
  "fulltext_url": null,
  "id": "3cwqnts81z22k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34252",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214730840",
  "pdf_url": "https://arxiv.org/pdf/2609.34252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3cwqnts81z22k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Heintze--Karcher-Type Inequalities for the $p$-Laplacian and Serrin-Type Rigidity",
  "title_text": "Heintze--Karcher-Type Inequalities for the p-Laplacian and Serrin-Type Rigidity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3cwqnts81z22k",
  "venue": "arXiv",
  "versions": []
}