{
  "abstract": "We establish a sharp reverse isoperimetric inequality for convex subsets of a triangle under a prescribed area constraint. Given a triangle $T$ and an area fraction $η\\in(0,1)$, we determine the set with maximal perimeter among convex bodies $K\\subset T$ satisfying $|K|=η|T|$ and characterize the equality cases. Every maximizer is a triangle, and the optimal configuration is obtained by retaining a longest side of $T$ and placing the third vertex on a shortest side, at the position determined by the area constraint. This characterization yields an explicit expression for the maximal perimeter in terms of $η$ and the side lengths of $T$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36220",
  "author_total": 3,
  "authors": [
    {
      "name": "Rida Ait El Manssour"
    },
    {
      "name": "Zakaria Fattah"
    },
    {
      "name": "Ilias Ftouhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hba240vkj4be.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36220",
  "fulltext_url": null,
  "id": "2hba240vkj4be",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36220",
  "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": "W7224134193",
  "pdf_url": "https://arxiv.org/pdf/2610.36220",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hba240vkj4be.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36220",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36220"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The reverse isoperimetric inequality for convex shapes included in a triangle",
  "title_text": "The reverse isoperimetric inequality for convex shapes included in a triangle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/2hba240vkj4be",
  "venue": "arXiv",
  "versions": []
}