{
  "abstract": "We extend the quermassintegral inequalities of our earlier work \\cite{GuanLi2009} from star-shaped domains to a substantially broader class of domains in Euclidean space, which we call spiral-star-shaped. A smooth domain is spiral-star-shaped if its boundary satisfies \\[ \\langle X+A X,ν\\rangle>0 \\] for some fixed skew-symmetric linear map $ A$, where $X$ is the position vector and $ν$ is the outward unit normal. The vector field $X+A X$ is conformal Killing, with dilation component $X$ and rotational component $A X$; its trajectories combine expansion and rotation, giving rise to the spiral terminology. When $A=0$, it reduces to ordinary star-shapedness, while nonzero $A$ allows domains that are not star-shaped in the usual radial sense. For smooth $k$-convex spiral-star-shaped domains, we prove long-time existence and exponential convergence to a round sphere for a locally constrained inverse curvature flow. The positive spiral support function provides the geometric control needed to treat initial hypersurfaces that need not be star-shaped in the usual sense. Monotonicity of the quermassintegrals along the flow yields sharp quermassintegral inequalities in this enlarged class, with equality if and only if the domain is a ball.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35394",
  "author_total": 1,
  "authors": [
    {
      "name": "Junfang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e18ey2gvr1kt4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35394",
  "fulltext_url": null,
  "id": "e18ey2gvr1kt4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35394",
  "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": "W7223808808",
  "pdf_url": "https://arxiv.org/pdf/2610.35394",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e18ey2gvr1kt4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35394",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35394"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The quermassintegral inequalities for k-convex spiral-star-shaped domains",
  "title_text": "The quermassintegral inequalities for k-convex spiral-star-shaped domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/e18ey2gvr1kt4",
  "venue": "arXiv",
  "versions": []
}