{
  "abstract": "Let S^{n+1}_{+} be the open hemisphere of the unit sphere S^{n+1} centred at o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^{alpha} {nu} of smooth, closed, strictly convex hypersurfaces enclosing o, where r is the geodesic distance to o. We consider both the supercritical regime beta>1+k {alpha} and the critical regime beta=1+k{alpha}, where beta is the growth order of the profile at the origin, f(r) almost equals r^{beta} as r descends to 0. Under the structural condition that f^{1/(1+k{alpha})} is convex, we prove long-time existence and preservation of strict convexity. The normalized radial function converges smoothly and exponentially to a constant: to 1 and to R_{infty}>0, resp. in different two cases. Thus the normalized radial graphs become round, while the original hypersurfaces contract to o.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31023",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongyi Sheng"
    },
    {
      "name": "Weimin Sheng"
    },
    {
      "name": "Jiazhuo Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54zs5re0n09y9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31023",
  "fulltext_url": null,
  "id": "54zs5re0n09y9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31023",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214575002",
  "pdf_url": "https://arxiv.org/pdf/2609.31023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54zs5re0n09y9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Non-homogeneous curvature flows in a hemisphere",
  "title_text": "Non-homogeneous curvature flows in a hemisphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/54zs5re0n09y9",
  "venue": "arXiv",
  "versions": []
}