{
  "abstract": "We establish a Loomis-Whitney inequality for the Reiter-Heisenberg groups $\\mathbb{G}_{qp}$, a family of step-two Carnot groups that includes the Heisenberg groups when $q=1$. The proof is based on the duality between Brascamp-Lieb inequalities and entropy subadditivity: we first derive the result for $\\mathbb{G}_{q1}$ from the known inequality on the first Heisenberg group, using conditional entropy and the invariance of differential entropy under volume-preserving diffeomorphisms; then we pass from $\\mathbb{G}_{q1}$ to $\\mathbb{G}_{qp}$ via a stability principle for Loomis-Whitney inequalities under finite central sums, which generalizes the argument in (Zhang, 2024 arXiv:2402.02749v2). As consequences, we obtain the associated geometric projection inequality, a Gagliardo-Nirenberg-Sobolev inequality, and an isoperimetric inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10091",
  "author_total": 2,
  "authors": [
    {
      "name": "Sheng-Chen Mao"
    },
    {
      "name": "Ye Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dwjyqnfft1f5a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10091",
  "fulltext_url": null,
  "id": "dwjyqnfft1f5a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10091",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212164980",
  "pdf_url": "https://arxiv.org/pdf/2609.10091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dwjyqnfft1f5a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Loomis-Whitney inequalities on Reiter-Heisenberg groups",
  "title_text": "Loomis-Whitney inequalities on Reiter-Heisenberg groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/dwjyqnfft1f5a",
  "venue": "arXiv",
  "versions": []
}