{
  "abstract": "We establish two types of Alexandrov--Fenchel inequalities for the weighted curvature integrals of static convex domains in space forms. The first type consists of a complete family of inequalities involving three weighted curvature integrals, with the second Minkowski type inequality of Xia [Calc. Var. Partial Differential Equations 55 (2016), Art. 96] and the weighted almost Schur lemma of Li and Xia [J. Differential Geom. 113 (2019), pp. 493--518] as special cases. The second type consists of a complete family of inequalities involving two weighted curvature integrals, confirming a conjectured geometric inequality by Hu and Li [Trans. Amer. Math. Soc. 375 (2022), pp. 5587--5615]. The key novelty lies in observing that, via the orthogonal projection map, the weighted curvature integrals for domains in space forms admit a natural interpretation in terms of mixed volumes of Euclidean convex bodies, thus reducing the problem to the classical Alexandrov--Fenchel inequalities in convex geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40087",
  "author_total": 1,
  "authors": [
    {
      "name": "Botong Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zacqkh70hp2v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40087",
  "fulltext_url": null,
  "id": "8zacqkh70hp2v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40087",
  "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.DG"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40087",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zacqkh70hp2v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40087",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40087"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Alexandrov--Fenchel inequalities for weighted curvature integrals in space forms",
  "title_text": "Alexandrov--Fenchel inequalities for weighted curvature integrals in space forms",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/8zacqkh70hp2v",
  "venue": "arXiv",
  "versions": []
}