{
  "abstract": "We study functional Blaschke--Santaló inequalities in which the inner product is replaced by a cost. An inequality on each orthant, combined with Steiner symmetrization, gives a sufficient condition for a cost inequality to hold for even convex functions. We apply this principle to a multiplicative cost defined on all orthants. Its second variation gives a weighted improvement of the Brascamp--Lieb inequality in the directions for which differentiation is justified. We also prove an $L^p$ version of the Fradelizi--Meyer theorem from a weighted volume-product inequality and derive the corresponding radial cost and Brascamp--Lieb inequalities. Explicit examples include anisotropic power and Cauchy densities, with dilation equality cases and a sharp obstruction below the coordinate exponent two. For the spherical logarithmic cost we compute an exact entropy--logdet deficit decomposition and the second-order deficit transverse to ellipsoids. We also explain the transport-entropy formulation and distinguish the restricted spectral question from the scalar $(B)$ property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19085",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexander V. Kolesnikov"
    },
    {
      "name": "Galyna V. Livshyts"
    },
    {
      "name": "Liran Rotem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8y600phrwg4d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19085",
  "fulltext_url": null,
  "id": "a8y600phrwg4d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19085",
  "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"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7222115557",
  "pdf_url": "https://arxiv.org/pdf/2610.19085",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8y600phrwg4d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19085",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19085"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Blaschke--Santaló inequalities with respect to costs",
  "title_text": "Blaschke--Santaló inequalities with respect to costs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/a8y600phrwg4d",
  "venue": "arXiv",
  "versions": []
}