{
  "abstract": "A Yau-type gradient estimate is proved for positive $p$-harmonic functions on complete Riemannian manifolds with compact boundary, under a Ricci lower bound on the Riemannian manifold and a mean curvature lower bound on the boundary, assuming the Dirichlet condition and a sign condition on the outward normal derivative. The result extends the estimate for harmonic functions by Kunikawa and Sakurai to the full range of $p$-Laplace operators and yields a Liouville theorem when the curvature hypotheses are nonnegative. The cutoff method of the linear theory does not extend when the exponent differs from two, since it requires a directional Hessian of the distance to the boundary that Laplacian comparison cannot control. That cutoff is replaced here by a radial barrier at the boundary and an intrinsic maximum principle in the interior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23471",
  "author_total": 1,
  "authors": [
    {
      "name": "Bingqi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/952rtgck1s2xm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23471",
  "fulltext_url": null,
  "id": "952rtgck1s2xm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23471",
  "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": "W7214049936",
  "pdf_url": "https://arxiv.org/pdf/2609.23471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/952rtgck1s2xm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Yau-type gradient estimates for p-harmonic functions on Riemannian manifolds with boundary under Dirichlet boundary condition",
  "title_text": "Yau-type gradient estimates for p-harmonic functions on Riemannian manifolds with boundary under Dirichlet boundary condition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/952rtgck1s2xm",
  "venue": "arXiv",
  "versions": []
}