{
  "abstract": "In 1952, Pólya proved the inequality $μ_2 < λ_1$ for the eigenvalues of Dirichlet and Neumann problems in domain $Ω\\subset \\mathbb{R}^d$, $d \\ge 2$. In 2026, Tang and Zhang proved the inequality $μ_3 < λ_1$ in the two-dimensional case. We show that $μ_3 < λ_1$ for $d\\ge 3$ as well.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13180",
  "author_total": 1,
  "authors": [
    {
      "name": "N. Filonov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yyf5whsmmpe2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13180",
  "fulltext_url": null,
  "id": "3yyf5whsmmpe2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13180",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221544871",
  "pdf_url": "https://arxiv.org/pdf/2610.13180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3yyf5whsmmpe2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.13180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13180"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the inequality $μ_3 < λ_1$ for the eigenvalues of the Laplace operator",
  "title_text": "On the inequality μ_3 < λ_1 for the eigenvalues of the Laplace operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/3yyf5whsmmpe2",
  "venue": "arXiv",
  "versions": []
}