{
  "abstract": "By studying the classical Minkowski's inequality, $4πA\\leq M^{2}$, relating area and mean curvature, in the particular case of convex surfaces of revolution, one is led to a functional inequality that holds for general functions. We state and prove this inequality obtaining a new proof of Minkowski's inequality in this particular case and we establish a sharp inequality between the Minkowski deficit of the surface and the isoperimetric deficit of any meridian curve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16792",
  "author_total": 3,
  "authors": [
    {
      "name": "Joaquim Bruna"
    },
    {
      "name": "Julià Cufí"
    },
    {
      "name": "Agustí Reventós"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/523hexbgwv543.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16792",
  "fulltext_url": null,
  "id": "523hexbgwv543",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16792",
  "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"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7213393349",
  "pdf_url": "https://arxiv.org/pdf/2609.16792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/523hexbgwv543.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Minkowski deficit for surfaces of revolution",
  "title_text": "On the Minkowski deficit for surfaces of revolution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/523hexbgwv543",
  "venue": "arXiv",
  "versions": []
}