{
  "abstract": "We establish a quantitative stability estimate for the first eigenvalue of the Laplacian with positive Robin boundary conditions. For every open set $Ω\\subset\\mathbb R^n$ of prescribed volume, we prove that \\[ λ_{1,β}(Ω)-λ_{1,β}(B) \\geq c\\|u_Ω-u_B\\|_{L^2(\\mathbb R^n)}^4, \\] where $B$ is a ball achieving the Fraenkel asymmetry of $Ω$, and $u_Ω$ and $u_B$ are nonnegative, $L^2$-normalized first Robin eigenfunctions, extended by zero outside their respective domains. The constant $c>0$ depends only on the dimension, the Robin parameter, and the prescribed volume. The exponent $4$ is optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28032",
  "author_total": 3,
  "authors": [
    {
      "name": "Carlo Nitsch"
    },
    {
      "name": "Cristina Trombetti"
    },
    {
      "name": "Federico Villone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0qkr66y4dt16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28032",
  "fulltext_url": null,
  "id": "b0qkr66y4dt16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28032",
  "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.AP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7223108318",
  "pdf_url": "https://arxiv.org/pdf/2610.28032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0qkr66y4dt16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28032"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Quantitative Robin Faber-Krahn Inequality in Terms of Eigenfunction Distance",
  "title_text": "A Quantitative Robin Faber-Krahn Inequality in Terms of Eigenfunction Distance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/b0qkr66y4dt16",
  "venue": "arXiv",
  "versions": []
}