{
  "abstract": "The aim of the paper is to highlight and standardize in a self-contained framework the connections between some properties associated with the Laplace-Beltrami operator on possibly incomplete Riemannian manifolds. We present both new and well-known characterizations of the positivity-preserving property, essential self-adjointness, and Liouville-type results for $L^2$-functions, using the latter to establish a clear hierarchy among these properties. Furthermore, we prove the stability of the essential self-adjointness of the Laplace-Beltrami operator on incomplete Riemannian manifolds under the removal of closed (possibly non-compact) subsets from a complete manifold, subject to suitable conditions on their (generalized) Hausdorff measure. With appropriate modifications, this framework is adapted throughout the paper to the general $L^p$-case for $p\\in (1,+\\infty)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29514",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrea Bisterzo"
    },
    {
      "name": "Salvatore Lincastri"
    },
    {
      "name": "Giona Veronelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43aecpv93mjar.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29514",
  "fulltext_url": null,
  "id": "43aecpv93mjar",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29514",
  "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",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7223221890",
  "pdf_url": "https://arxiv.org/pdf/2610.29514",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43aecpv93mjar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29514",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29514"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$L^p$-Liouville properties and realizations of Schrödinger operators on incomplete Riemannian manifolds",
  "title_text": "L^p-Liouville properties and realizations of Schrödinger operators on incomplete Riemannian manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/43aecpv93mjar",
  "venue": "arXiv",
  "versions": []
}