{
  "abstract": "Higher order sharp Sobolev and local Sobolev type inequalities for log-concave functions are established. The new inequalities directly imply the isoperimetric inequalities by Bollobás and Thomason in 1995, by Liakopoulos in 2019, and the recently discovered local isoperimetric inequalities from [1]. In order to do so, we make use of three ingredients. First, sets of functional inequalities proven by Alonso-Gutiérrez, Bernués, Brazitikos and Carbery in 2021. Second, a multidimensional polynomial optimization result that originated in [1] and was initiated by Bollobás and Thomason. Third, a new integral formula for the projection of a log-concave function that links the geometric part with the more functional versions via some dependence on the Hessian matrix restricted to subspaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32886",
  "author_total": 3,
  "authors": [
    {
      "name": "Luis J. Alías"
    },
    {
      "name": "Bernardo González Merino"
    },
    {
      "name": "Beatriz Marín Gimeno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnb2yb52cvpan.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32886",
  "fulltext_url": null,
  "id": "bnb2yb52cvpan",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32886",
  "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.DG"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7223696823",
  "pdf_url": "https://arxiv.org/pdf/2610.32886",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnb2yb52cvpan.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.32886",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32886"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sobolev inequalities for sections and projections of log-concave functions",
  "title_text": "Sobolev inequalities for sections and projections of log-concave functions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bnb2yb52cvpan",
  "venue": "arXiv",
  "versions": []
}