{
  "abstract": "We establish sharp Alexandrov--Fenchel inequalities for closed, embedded, axisymmetric hypersurfaces Sigma in n+1 dimensional Euclidean space R^{n+1}, the dimension n > or = 2, with admissible C^{1,1} profiles. Let H_j be the j-th normalized mean curvature. If Sigma is axiconvex, i.e., every hyperplane orthogonal to the symmetry axis meets the enclosed domain in an n-dimensional ball or empty, then \\[\\left(\\frac{\\int_ΣH_\\ell\\,dA}{|\\mathbb S^n|}\\right)^{1/(n-\\ell)} \\le \\left(\\frac{\\int_ΣH_k\\,dA}{|\\mathbb S^n|}\\right)^{1/(n-k)}, \\qquad 0\\le\\ell<k\\le n-1. \\] Without axiconvexity, the inequalities hold for sign-corrected integrals \\[\\int_Σ\\varepsilon_θ^{\\,j}H_j\\,dA,\\] where varepsilon_{theta}= {sgn}(sin {theta}) denotes the sign of the azimuthal principal curvatures. As applications, the Alexandrov--Fenchel inequalities remain valid whenever both l and k are even. Equality in each of the above inequalities holds if and only if Sigma is a round sphere. The proof adapts the rearrangement and tangent angle folding approach of Dalphin-Henrot-Masnou-Takahashi from surfaces of revolution in R^3 to n-dimensional axisymmetric hypersurfaces in R^{n+1}. The higher-dimensional construction uses weighted monotone rearrangement to produce convex comparison bodies with C^{1,1} boundaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15311",
  "author_total": 2,
  "authors": [
    {
      "name": "Weimin Sheng"
    },
    {
      "name": "Yinhang Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0eny2brgdmwsd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15311",
  "fulltext_url": null,
  "id": "0eny2brgdmwsd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15311",
  "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|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221782018",
  "pdf_url": "https://arxiv.org/pdf/2610.15311",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0eny2brgdmwsd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15311",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15311"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Alexandrov--Fenchel inequalities for closed axisymmetric hypersurfaces",
  "title_text": "Alexandrov--Fenchel inequalities for closed axisymmetric hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0eny2brgdmwsd",
  "venue": "arXiv",
  "versions": []
}