{
  "abstract": "We establish stability properties of near-extremisers for the Loomis--Whitney inequality and its adjoint, presenting our results in the general framework of Finner. In particular, we show that a function nearly achieves equality in the adjoint Finner inequality if and only if it is near to being an indicator function of a cartesian product. As an application, we obtain new lower bounds for the classical $k$-plane transform on $L^p(\\mathbb{R}^d)$, modestly improving those obtained recently by Tao and the first author. We also present an alternative approach to such improvements based on stability in the setting of the Brascamp--Lieb inequality and the theory of fusion frames. We conclude with an interpretation of our $k$-plane transform estimates as adjoint forms of the continuous Brascamp--Lieb inequalities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29041",
  "author_total": 2,
  "authors": [
    {
      "name": "Jonathan Bennett"
    },
    {
      "name": "Sewook Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6x82whxjvh9qt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29041",
  "fulltext_url": null,
  "id": "6x82whxjvh9qt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29041",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7223207983",
  "pdf_url": "https://arxiv.org/pdf/2610.29041",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6x82whxjvh9qt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29041",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29041"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability for the adjoint Finner inequality and improved lower bounds on the $k$-plane transform",
  "title_text": "Stability for the adjoint Finner inequality and improved lower bounds on the k-plane transform",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/6x82whxjvh9qt",
  "venue": "arXiv",
  "versions": []
}