{
  "abstract": "We show that the spectrum of the Dirichlet-biLaplacian can be quantitatively bounded from below in terms of the inradius only, for a general open set in dimensions $2$ and $3$. For the same dimensions, we also extend this result to fractional powers $s$ of the Laplacian, with $N/2<s<2$. The resulting estimate comes with a constant having the correct asymptotic behavior as $s$ approaches the two endpoints $N/2$ and $2$. The proofs exploit capacitary techniques in the vein of Maz'ya.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16485",
  "author_total": 3,
  "authors": [
    {
      "name": "Francesca Bianchi"
    },
    {
      "name": "Francesco Bozzola"
    },
    {
      "name": "Lorenzo Brasco"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6z6z0g0t81g2p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16485",
  "fulltext_url": null,
  "id": "6z6z0g0t81g2p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16485",
  "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.FA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221833995",
  "pdf_url": "https://arxiv.org/pdf/2610.16485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6z6z0g0t81g2p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A geometric lower bound for the clamped plate eigenvalue problem in low dimensions and extensions",
  "title_text": "A geometric lower bound for the clamped plate eigenvalue problem in low dimensions and extensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6z6z0g0t81g2p",
  "venue": "arXiv",
  "versions": []
}