{
  "abstract": "We obtain two quantitative results related to classical rearrangement inequalities for the first Dirichlet eigenvalue. The first one is a quantitative version of Chiti's reverse Hölder inequality. More precisely, for every $1\\le q<p<\\infty$, we prove that the deficit controls, up to translations, the $L^q$ distance between a first eigenfunction of a bounded domain and the first eigenfunction of the ball having the same first eigenvalue. The second result concerns the Kohler--Jobin inequality and gives a quantitative estimate in terms of the $L^\\infty\\!\\to L^2$ distance between the corresponding Dirichlet resolvents. In both cases, the main idea is to find a suitable superlevel set of the first eigenfunction which is almost optimal for the Faber-Krahn inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31063",
  "author_total": 7,
  "authors": [
    {
      "name": "Vincenzo Amato"
    },
    {
      "name": "Luca Barbato"
    },
    {
      "name": "Emanuele Cristoforoni"
    },
    {
      "name": "Alba Lia Masiello"
    },
    {
      "name": "Carlo Nitsch"
    },
    {
      "name": "Cristina Trombetti"
    },
    {
      "name": "Federico Villone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ewmthmg3bh5zv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31063",
  "fulltext_url": null,
  "id": "ewmthmg3bh5zv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31063",
  "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",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7223265575",
  "pdf_url": "https://arxiv.org/pdf/2610.31063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ewmthmg3bh5zv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A unified quantitative approach to Chiti and Kohler--Jobin inequalities",
  "title_text": "A unified quantitative approach to Chiti and Kohler--Jobin inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/ewmthmg3bh5zv",
  "venue": "arXiv",
  "versions": []
}