{
  "abstract": "Consider a subcritical functional $Q$ associated with a $p$-Schrödinger operator defined on a domain $Ω$ in noncompact Riemannian manifold. Employing the supersolution construction, we obtain a family of strictly positive critical Hardy weights for $Q$. The construction is based on the Green potential, with a strictly positive charge, which is assumed to vanish at infinity. An interesting new feature of this family, depending on a parameter $0\\leq \\varepsilon\\leq 1$, is the transition from positive-criticality to null-criticality at $\\varepsilon=0$. Moreover, we show that the best Hardy constant for this family is given by $c=[(p-1)/p]^{p-1}$, and that for $\\varepsilon=0$ the corresponding Hardy weight is optimal. We furthermore, prove an analogous result on graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02365",
  "author_total": 3,
  "authors": [
    {
      "name": "Ujjal Das"
    },
    {
      "name": "Matthias Keller"
    },
    {
      "name": "Yehuda Pinchover"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ej83krrgxqygx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02365",
  "fulltext_url": null,
  "id": "ej83krrgxqygx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02365",
  "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": "W7220441143",
  "pdf_url": "https://arxiv.org/pdf/2610.02365",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ej83krrgxqygx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02365",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02365"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strictly positive optimal Hardy weights on manifolds and graphs via Green potential",
  "title_text": "Strictly positive optimal Hardy weights on manifolds and graphs via Green potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/ej83krrgxqygx",
  "venue": "arXiv",
  "versions": []
}