{
  "abstract": "We prove a strengthened Brascamp--Lieb inequality for even log-concave measures whose positive sublevel bodies satisfy the local logarithmic Brunn--Minkowski inequality. The conclusion can be written either by adding a rank-one term to the Hessian of the potential or by adding an explicit nonnegative remainder to the variance. The proof uses sublevel volume variations, a one-dimensional Brascamp--Lieb inequality, and the coarea formula. The derivative of the potential under dilations gives an equality function whenever it is square-integrable. For potentials homogeneous of degree greater than one, we obtain a sharp radial remainder.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21669",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander V. Kolesnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqcvp782sz3zh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21669",
  "fulltext_url": null,
  "id": "aqcvp782sz3zh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21669",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7222755349",
  "pdf_url": "https://arxiv.org/pdf/2610.21669",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqcvp782sz3zh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21669",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21669"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A logarithmic Brascamp--Lieb variance inequality",
  "title_text": "A logarithmic Brascamp--Lieb variance inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/aqcvp782sz3zh",
  "venue": "arXiv",
  "versions": []
}