{
  "abstract": "Bär has shown that a fixed boundary metric and a scalar-curvature lower bound do not generally bound total mean curvature from above. We extend this unboundedness to every smooth compact connected manifold of dimension $n\\ge3$ with nonempty boundary and every prescribed boundary metric, using scalar-flat metrics. While Bär's examples use warped products, our construction uses a nonzero cubic variation of total mean curvature near a flat product, followed by localization and conformal correction. We also construct arbitrarily $C^k$-small perturbations of the flat torical half-cylinder with nonnegative scalar curvature, unchanged boundary metric, an exact product end, and positive total boundary mean curvature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04762",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhixin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15h8dh4s3nk12.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04762",
  "fulltext_url": null,
  "id": "15h8dh4s3nk12",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04762",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04762",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15h8dh4s3nk12.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04762",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04762"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Unbounded total mean curvature with prescribed boundary metric",
  "title_text": "Unbounded total mean curvature with prescribed boundary metric",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/15h8dh4s3nk12",
  "venue": "arXiv",
  "versions": []
}