{
  "abstract": "We establish Wulff rigidity for overdetermined anisotropic $k$-Hessian equations associated with a smooth and strongly convex Finsler gauge. The solutions are subject to homogeneous Dirichlet boundary and a prescribed anisotropic gradient condition on a smooth domain. We prove that the domain must be a Wulff shape. The same rigidity holds under a prescribed positive weighted Neumann-type condition. These results extend the Wulff rigidity for the endpoint cases $k=1$ (Cianchi--Salani, \\emph{Math. Ann.}, 2009; Wang--Xia \\emph{Arch. Ration. Mech. Anal.}, 2011) and $k=n$ ( Cianchi--Salani, \\emph{J. Funct. Anal.}, 2023) to the intermediate cases $2\\le k<n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39756",
  "author_total": 2,
  "authors": [
    {
      "name": "Lichun Liang"
    },
    {
      "name": "Yanjun Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99421xfdmnarx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39756",
  "fulltext_url": null,
  "id": "99421xfdmnarx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39756",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99421xfdmnarx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Wulff Rigidity for Overdetermined Anisotropic $k$-Hessian Equations",
  "title_text": "Wulff Rigidity for Overdetermined Anisotropic k-Hessian Equations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/99421xfdmnarx",
  "venue": "arXiv",
  "versions": []
}