{
  "abstract": "We prove that a stable noncompact hypersurface with constant anisotropic mean curvature in $\\mathbb{R}^{n+1}$ has only one end for $n \\le 6$, under a natural ellipticity condition on the anisotropy. This provides an anisotropic counterpart of the one-end theorem for stable constant mean curvature hypersurfaces. We remark that the result is also new in $\\mathbb R^7 (n=6)$, in the case of anisotropic minimal hypersurfaces. The proof relies on the existence of a Sobolev-type inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27480",
  "author_total": 1,
  "authors": [
    {
      "name": "Claudia Pontuale"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ypbfy739tp5w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27480",
  "fulltext_url": null,
  "id": "3ypbfy739tp5w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27480",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214201393",
  "pdf_url": "https://arxiv.org/pdf/2609.27480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ypbfy739tp5w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the structure of stable constant anisotropic mean curvature hypersurfaces",
  "title_text": "On the structure of stable constant anisotropic mean curvature hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/3ypbfy739tp5w",
  "venue": "arXiv",
  "versions": []
}