{
  "abstract": "Among connected, planar sets, the ratio between the isoperimetric deficit and the squared barycentric asymmetry is known to be bounded from below by a strictly positive constant (as proved in recent papers by Bianchini-Croce-Henrot and Gambicchia-Pratelli). This opens the natural question whether the infimum is attained at some set. In this paper, we prove that a minimizer for this ratio actually exists, and moreover it is simply connected.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15088",
  "author_total": 3,
  "authors": [
    {
      "name": "Chiara Gambicchia"
    },
    {
      "name": "Aldo Pratelli"
    },
    {
      "name": "Clara Torres-Latorre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07pdrefcy4d35.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15088",
  "fulltext_url": null,
  "id": "07pdrefcy4d35",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15088",
  "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.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221770015",
  "pdf_url": "https://arxiv.org/pdf/2610.15088",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/07pdrefcy4d35.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15088",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15088"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On the minimizer of the barycentric isoperimetric ratio among connected planar sets",
  "title_text": "On the minimizer of the barycentric isoperimetric ratio among connected planar sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/07pdrefcy4d35",
  "venue": "arXiv",
  "versions": []
}