{
  "abstract": "Let $M$ be a connected complete noncompact Riemannian manifold without boundary, and let $V_o(R)$ denote its ball volume. We prove Liouville theorems without any curvature assumption. For $p>1$ and $q>p-1$, divergence of $\\int^\\infty R^{pq/(p-1)-1}V_o(R)^{-(q-p+1)/(p-1)}\\dd R$ forces every nonnegative Sobolev weak supersolution of $-Δ_pu\\ge u^q$ to vanish. For $q>\\max\\{1,p-1\\}$, divergence of $\\int^\\infty R^{p-1}V_o(R)^{-(q-p+1)}\\dd R$ forces every nonnegative global distributional energy supersolution of $u_t-Δ_pu\\ge u^q$ to vanish. Consequently, the corresponding Cauchy problem has no global solution in this class with a nonzero nonnegative local $L^1$ initial trace.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22803",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongheng Qin"
    },
    {
      "name": "Yuhua Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/59r155dwmmzjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22803",
  "fulltext_url": null,
  "id": "59r155dwmmzjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22803",
  "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"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222962311",
  "pdf_url": "https://arxiv.org/pdf/2610.22803",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/59r155dwmmzjd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22803",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Integral Volume Criteria for Semilinear and Quasilinear Liouville Theorems on Complete Manifolds",
  "title_text": "Integral Volume Criteria for Semilinear and Quasilinear Liouville Theorems on Complete Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/59r155dwmmzjd",
  "venue": "arXiv",
  "versions": []
}