{
  "abstract": "For $n\\geq 2$, we study the optimal function $φ_n$ in the Brunn-Minkowski inequality for $θ$-convolution bodies $|K+_θL|^{1/n}\\geqφ_n(θ)(|K|^{1/n}+|L|^{1/n})$ for any convex bodies $K,L\\subset\\mathbb{R}^n$. We improve the known lower bound for every $0<θ<(3/4)^n$ and determine $φ_n$ on an interval strictly containing $[(2/3)^n,1]$. For $θ<1$ in this interval, equality holds if and only if $K$ and $-L$ are translates of the same $n$-dimensional simplex. The proof reduces the geometric problem to a sharp one-dimensional estimate for nonnegative concave functions under a weighted integral constraint.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37066",
  "author_total": 1,
  "authors": [
    {
      "name": "Javier Martín Goñi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qce25dtefkyb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37066",
  "fulltext_url": null,
  "id": "7qce25dtefkyb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37066",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7224119112",
  "pdf_url": "https://arxiv.org/pdf/2610.37066",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qce25dtefkyb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37066",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37066"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Improved Brunn--Minkowski inequality for $θ$-convolution bodies",
  "title_text": "Improved Brunn--Minkowski inequality for θ-convolution bodies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7qce25dtefkyb",
  "venue": "arXiv",
  "versions": []
}