{
  "abstract": "We study dimensional concavity properties of even log-concave measures within the framework of weighted centroaffine differential geometry. We express the relevant local concavity inequalities in terms of a weighted Hilbert--Brunn--Minkowski operator and establish an anisotropic Poincaré inequality for odd functions and a strengthened Brascamp--Lieb inequality for even functions. As applications, we obtain quantitative dimensional concavity estimates for a class of geometric measures and measures with pinched Hessian, extending results of Cordero-Erausquin and Rotem for rotationally invariant measures and Eskenazis and Moschidis for the Gaussian measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08283",
  "author_total": 3,
  "authors": [
    {
      "name": "Sotiris Armeniakos"
    },
    {
      "name": "Alexander V. Kolesnikov"
    },
    {
      "name": "Jacopo Ulivelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1y9ywfgcda1rm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08283",
  "fulltext_url": null,
  "id": "1y9ywfgcda1rm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08283",
  "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.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08283",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1y9ywfgcda1rm.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08283",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08283"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A centroaffine perspective on improved Brascamp--Lieb and dimensional Brunn--Minkowski inequalities",
  "title_text": "A centroaffine perspective on improved Brascamp--Lieb and dimensional Brunn--Minkowski inequalities",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/1y9ywfgcda1rm",
  "venue": "arXiv",
  "versions": []
}