{
  "abstract": "Given a smooth domain $D\\subset\\mathbb S^{N-1}$, $N\\geq 3$, and a positive constant $H$, we study radial graphs over $D$ with constant mean curvature $H$ which meet orthogonally the boundary of the cone spanned by $D$. The corresponding problem is given by a quasilinear elliptic equation on $D$ with homogeneous Neumann boundary condition. We investigate the structure of the solution set under smooth perturbations of the domain which are parametrized by an open set of $C^{3,α}$-diffeomorphisms of the sphere. After pulling the equation back to a fixed reference domain, we apply a classical transversality theorem and prove that, in the class of domains for which $N-1$ does not belong to the Neumann spectrum of the Laplace-Beltrami operator, there is a residual set for which every solution is nondegenerate. A consequence of our result is that, for every such domain and every $R>0$, the set of solutions whose $C^{2,α}$-norm is bounded by $R$ is finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14755",
  "author_total": 2,
  "authors": [
    {
      "name": "Alessandro Iacopetti"
    },
    {
      "name": "Filomena Pacella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ctyextv141byv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14755",
  "fulltext_url": null,
  "id": "ctyextv141byv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14755",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221775872",
  "pdf_url": "https://arxiv.org/pdf/2610.14755",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ctyextv141byv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14755",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14755"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Generic nondegeneracy of constant mean curvature radial graphs",
  "title_text": "Generic nondegeneracy of constant mean curvature radial graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ctyextv141byv",
  "venue": "arXiv",
  "versions": []
}