{
  "abstract": "We prove that standard $k$-bubbles uniquely minimize perimeter in $\\mathbb R^n$ and $\\mathbb S^n$ for $n\\ge2$ and $1\\le k\\le n$, and that standard double bubbles uniquely minimize perimeter in $\\mathbb H^n$ for $n\\ge3$. For nonnegative curvature, the proof combines the structure and spectral theory of Milman--Neeman with a uniform semialgebraic exceptional set, an almost-everywhere profile comparison, and localized variational arguments. A curvature-variable lift gives a uniformly elliptic comparison at the Euclidean limit. The independent hyperbolic argument uses the rotational structure of Cotton--Freeman, a scalar meridian force potential, and a transverse conformal variation. The critical range $k=n+1$ in $\\mathbb R^n$ and $\\mathbb S^n$, and hyperbolic clusters with more than two finite cells, are not covered.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00252",
  "author_total": 1,
  "authors": [
    {
      "name": "Zihao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mysce1n8jm5p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00252",
  "fulltext_url": null,
  "id": "2mysce1n8jm5p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00252",
  "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"
    ],
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mysce1n8jm5p.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Noncritical multi-bubbles and hyperbolic double bubbles",
  "title_text": "Noncritical multi-bubbles and hyperbolic double bubbles",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/2mysce1n8jm5p",
  "venue": "arXiv",
  "versions": []
}