{
  "abstract": "We give a direct proof of the weak interlacing inequalities \\[ω_p\\leq\\widetildeω_p\\leqω_{p+1}\\] between the volume and half-volume spectra of a closed connected Riemannian manifold $M^{n+1}$, $n+1\\geq3$. We also prove that, for a residual set of smooth metrics, the area of every smooth embedded half-volume CMC boundary lies outside the rational span of the areas of smooth closed embedded minimal hypersurfaces. For dimensions $3\\le n+1\\le 5$, these results yield strict interlacing for generic metrics and a lower bound of order $A^{n+1}$ for the number of distinct half-volume CMC boundaries with area at most $A$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07801",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaoxiang Jiao"
    },
    {
      "name": "Hangyue Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zqjnebwegp1e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07801",
  "fulltext_url": null,
  "id": "4zqjnebwegp1e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07801",
  "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/2611.07801",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zqjnebwegp1e.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07801",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07801"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Interlacing of the Volume and Half-Volume Spectra",
  "title_text": "Interlacing of the Volume and Half-Volume Spectra",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/4zqjnebwegp1e",
  "venue": "arXiv",
  "versions": []
}