{
  "abstract": "We describe the $L^p$-parabolicity of a Riemannian manifold in terms of a unified theory of nonlinear $L^p$-capacities, for the whole range $1\\leq p\\leq \\infty$. For example, the \\(L^{1}\\)-parabolicity is equivalent to the usual notion of parabolicity/recurrence, while \\(L^{2}\\)-parabolicity is equivalent to biparabolicity. For any $1\\leq p\\leq \\infty,$ the $L^p$-parabolicity turns out to be equivalent to the $L^q$-Liouville property for positive superharmonic functions, where $p$ and $q$ are Hölder conjugate exponents. We also provide a new capacitary characterization of the $L^1$-Liouville property. Finally we obtain an almost optimal volume growth condition for the $L^p$-parabolicity for $1<p\\leq 2$ as well as a sharp volume condition for all $1<p<\\infty$ for manifolds of non-negative Ricci curvature and for model manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27302",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexander Grigor'yan"
    },
    {
      "name": "Leandro F. Pessoa"
    },
    {
      "name": "Alberto G. Setti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11hqkbqde4782.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27302",
  "fulltext_url": null,
  "id": "11hqkbqde4782",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27302",
  "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": "W7223132980",
  "pdf_url": "https://arxiv.org/pdf/2610.27302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11hqkbqde4782.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$L^{p}$-parabolicity of Riemannian manifolds",
  "title_text": "L^p-parabolicity of Riemannian manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/11hqkbqde4782",
  "venue": "arXiv",
  "versions": []
}