{
  "abstract": "We study quermassintegral-preserving curvature flows in $\\mathbb H^{n+1}$, $n\\geq3$, driven by the curvature quotient $(E_k/E_\\ell)^{1/(k-\\ell)}$. For $1\\leq\\ell<k$ with $k+\\ell\\leq n$, we prove that positive sectional curvature is preserved. Starting from a smooth closed strictly convex hypersurface with positive sectional curvature, the flow exists for all time and converges smoothly and exponentially to a geodesic sphere. As an application, we establish sharp Alexandrov--Fenchel inequalities between $W_k$ and $W_\\ell$ for smooth bounded convex domains whose boundaries have nonnegative sectional curvature, whenever $0\\leq\\ell<k\\leq n$ and $k+\\ell\\leq n$. Equality holds if and only if the domain is a geodesic ball. Together with previously known cases, these inequalities give the full family of Alexandrov--Fenchel inequalities for this class of domains in $\\mathbb H^6$. We also construct counterexamples showing that $k+\\ell\\leq n$ is the optimal range for preservation of positive sectional curvature by these flows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35707",
  "author_total": 4,
  "authors": [
    {
      "name": "Tianci Luo"
    },
    {
      "name": "Yong Wei"
    },
    {
      "name": "Ruijia Zhang"
    },
    {
      "name": "Rong Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/646f9c610xdga.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35707",
  "fulltext_url": null,
  "id": "646f9c610xdga",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35707",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223977601",
  "pdf_url": "https://arxiv.org/pdf/2610.35707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/646f9c610xdga.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.35707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35707"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Curvature quotient flows and Alexandrov--Fenchel inequalities in hyperbolic space",
  "title_text": "Curvature quotient flows and Alexandrov--Fenchel inequalities in hyperbolic space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/646f9c610xdga",
  "venue": "arXiv",
  "versions": []
}