{
  "abstract": "In this paper, we introduce a concept of modified curvature measures for h-convex domains in hyperbolic space and prove a shifted version of the generalized Alexandrov theorem, which characterizes geodesic balls in hyperbolic space via modified curvature measures. This result generalizes the classical work of Kohlmann (1998). We further investigate a volume-preserving shifted $α$-Gauss curvature flow for strictly h-convex hypersurfaces in hyperbolic space and prove that for any $α>0$ the solution exists for all time and converges smoothly to a geodesic sphere. The theory of modified curvature measures developed in the first part serves as a key ingredient in characterizing the Hausdorff limit shape of the flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18423",
  "author_total": 1,
  "authors": [
    {
      "name": "Xinxiu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3esw7knadggw7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18423",
  "fulltext_url": null,
  "id": "3esw7knadggw7",
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  "landing_url": "https://arxiv.org/abs/2610.18423",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7221769220",
  "pdf_url": "https://arxiv.org/pdf/2610.18423",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3esw7knadggw7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18423",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18423"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Curvature measures and volume preserving flows in h-convex geometry",
  "title_text": "Curvature measures and volume preserving flows in h-convex geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/3esw7knadggw7",
  "venue": "arXiv",
  "versions": []
}