{
  "abstract": "For $n\\ge2$, we prove that the $C^2$ boundary of a bounded nonempty open set in $\\mathbb H^n$ is volume-preserving stable if and only if it is a Pansu sphere up to left translation and Heisenberg dilation. The proof combines centre reconstruction with a volume-constrained test field derived from Pansu dilation. Consequently, every isoperimetric region admitting an open representative with $C^2$ boundary is a Pansu ball up to these symmetries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03900",
  "author_total": 3,
  "authors": [
    {
      "name": "Wei-Chun Chen"
    },
    {
      "name": "Wei-Ting Kao"
    },
    {
      "name": "Chun-Kai Lien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e04xc904gm7k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03900",
  "fulltext_url": null,
  "id": "1e04xc904gm7k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03900",
  "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": "W7220671467",
  "pdf_url": "https://arxiv.org/pdf/2610.03900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e04xc904gm7k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stable Rigidity in the Heisenberg Groups",
  "title_text": "Stable Rigidity in the Heisenberg Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1e04xc904gm7k",
  "venue": "arXiv",
  "versions": []
}