{
  "abstract": "For a given $λ> 0$, a convex body in $\\mathbb{R}^n$ is called $λ$-convex if it is the intersection of balls of radius $1/λ$. We show that among all $λ$-convex bodies in $\\mathbb R^n$ of a given surface area, volume is minimized by the $λ$-convex lens, that is, the intersection of two balls of radius $1/λ$. This confirms a conjecture of Borisenko in all dimensions $n \\geq 2$. Moreover, we extend this reverse isoperimetric inequality to all model spaces of constant curvature in arbitrary dimension and arbitrary $λ> 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40291",
  "author_total": 2,
  "authors": [
    {
      "name": "Kostiantyn Drach"
    },
    {
      "name": "Kateryna Tatarko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2a5k0pdhtsgfp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40291",
  "fulltext_url": null,
  "id": "2a5k0pdhtsgfp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40291",
  "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.DG"
    ],
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40291",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2a5k0pdhtsgfp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40291",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40291"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A complete solution to the reverse isoperimetric problem for $λ$-convex bodies",
  "title_text": "A complete solution to the reverse isoperimetric problem for λ-convex bodies",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2a5k0pdhtsgfp",
  "venue": "arXiv",
  "versions": []
}