{
  "abstract": "We construct a sequence $\\{\\Sigma _\\ell \\}_{\\ell =1}^\\infty $ of closed, axially symmetric surfaces $\\Sigma _\\ell \\subset \\mathbb{R}^{3}$ that converges to the unit sphere in $W^{2,p}\\cap C^{1}$ for every $p\\in [1,\\infty )$ and such that, for every $\\ell $, $$ \\begin{align*} & \\int_{\\Sigma_{\\ell}}H_{\\Sigma_\\ell}-\\sqrt{16\\,\\pi\\,|\\Sigma_{\\ell}|}<0, \\end{align*} $$ where $H_{\\Sigma _\\ell }$ is the mean curvature of $\\Sigma _\\ell $. This shows that unless additional convexity assumptions are imposed, the Minkowski inequality with optimal constant fails even for perturbations of a round sphere that are small in $W^{2,p}\\cap C^{1}$.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Stanford University , Building 380, Stanford, CA 94305, USA",
    "Faculty of Mathematics, University of Vienna , Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Otis Chodosh",
      "orcid": "0000-0002-6124-7889"
    },
    {
      "affs": [
        1
      ],
      "name": "Michael Eichmair",
      "orcid": "0000-0001-7993-9536"
    },
    {
      "affs": [
        1
      ],
      "name": "Thomas Koerber",
      "orcid": "0000-0003-1676-0824"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aphz2dg4gfdgj.bib",
  "cited_by": 5,
  "doi": "10.1093/imrn/rnag142",
  "fulltext_url": null,
  "id": "aphz2dg4gfdgj",
  "issns": [
    "1073-7928",
    "1687-0247"
  ],
  "landing_url": "https://doi.org/10.1093/imrn/rnag142",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
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  "openalex": "W4379961422",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-16",
  "publisher": "Oxford University Press",
  "ris": "https://research.draconitic.com/paper/aphz2dg4gfdgj.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W4379961422",
      "source": "openalex",
      "url": "https://doi.org/10.1093/imrn/rnag142"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Geometric Analysis and Curvature Flows",
      "subfield": "general"
    }
  ],
  "title": "On the Minkowski inequality near the sphere",
  "title_text": "On the Minkowski inequality near the sphere",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:22Z",
  "url": "https://research.draconitic.com/paper/aphz2dg4gfdgj",
  "venue": "International Mathematics Research Notices",
  "versions": []
}