{
  "abstract": "We prove the Alexandrov--Fenchel inequalities between any two spherical quermassintegrals for smooth weakly convex domains contained in an open hemisphere, with equality if and only if the domain is a geodesic ball. For strictly convex hypersurfaces, we introduce a globally constrained curvature flow which preserves one quermassintegral and decreases the next one. We establish uniform curvature estimates by combining a pinching estimate, a support function argument, and spherical polarity. As a consequence, the flow exists for all time and converges smoothly and exponentially to a geodesic sphere. The monotonicity of the quermassintegrals gives the full family of Alexandrov--Fenchel inequalities. A short-time mean curvature flow approximation and a localized rigidity argument extend the result, including the equality characterization, to weakly convex domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13829",
  "author_total": 3,
  "authors": [
    {
      "name": "Tianci Luo"
    },
    {
      "name": "Yong Wei"
    },
    {
      "name": "Rong Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bcvbx5220h925.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13829",
  "fulltext_url": null,
  "id": "bcvbx5220h925",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13829",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213349758",
  "pdf_url": "https://arxiv.org/pdf/2609.13829",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bcvbx5220h925.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13829",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13829"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Alexandrov--Fenchel inequalities for convex domains in the sphere",
  "title_text": "Alexandrov--Fenchel inequalities for convex domains in the sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/bcvbx5220h925",
  "venue": "arXiv",
  "versions": []
}