{
  "abstract": "We determine the growth scale of the optimal constants in the real anisotropic Bohnenblust--Hille inequality. For an exponent vector $\\mathbf q^{(m)}$, write $C_{\\mathbf q^{(m)}}^{(m)}$ for its optimal constant and $d_m$ for its diameter. These constants are superpolynomial precisely when $m d_m/\\log m\\to\\infty$; throughout this regime, their logarithm has the sharp scale $m d_m$. If also $d_m\\to0$, then $\\log C_{\\mathbf q^{(m)}}^{(m)}/(m d_m)$ lies asymptotically in the interval $\\left[\\frac{\\log 2}{4},\\frac{2-\\log 2-γ}{4}\\right]$, where $γ$ is the Euler--Mascheroni constant; this interval has width less than $10^{-2}$. We also solve the extremal problems at fixed diameter and fixed total deficit. The normalized reciprocal-deficit profiles order the canonically arranged optimal constants by majorization, yield exact formulas on a full-dimensional region, and recover the lower coefficient $(\\log 2)/4$ throughout a broad class of anisotropic regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04143",
  "author_total": 5,
  "authors": [
    {
      "name": "Daniel Nunez-Alarcon"
    },
    {
      "name": "Daniel M. Pellegrino"
    },
    {
      "name": "Joedson Silva dos Santos"
    },
    {
      "name": "Diana Marcela Serrano-Rodriguez"
    },
    {
      "name": "Eduardo V. Teixeira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s6za6qtezvc0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04143",
  "fulltext_url": null,
  "id": "1s6za6qtezvc0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04143",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7208736922",
  "pdf_url": "https://arxiv.org/pdf/2609.04143",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s6za6qtezvc0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.04143",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04143"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Geometry of Real Anisotropic Bohnenblust--Hille Constants",
  "title_text": "The Geometry of Real Anisotropic Bohnenblust--Hille Constants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/1s6za6qtezvc0",
  "venue": "arXiv",
  "versions": []
}