{
  "abstract": "We consider the isoperimetric problem with planar density equal to 1 on a horizontal strip and to a constant $λ>1$ outside the strip. We resolve a conjecture made by Cañete-Miranda Jr-Vittone by showing that every four-arc region admits a three-arc competitor with the same weighted area and strictly smaller weighted perimeter. The argument applies to every $λ>1$ and gives an explicit positive lower bound for the perimeter difference.",
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  "article_type": null,
  "arxiv": "2609.36564",
  "author_total": 4,
  "authors": [
    {
      "name": "Skilyn Leon"
    },
    {
      "name": "Rosa Pavlak"
    },
    {
      "name": "Evelyn Pulla"
    },
    {
      "name": "Xi Sisi Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5907f8wxvd9ss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36564",
  "fulltext_url": null,
  "id": "5907f8wxvd9ss",
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  "landing_url": "https://arxiv.org/abs/2609.36564",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7214965804",
  "pdf_url": "https://arxiv.org/pdf/2609.36564",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5907f8wxvd9ss.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36564",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36564"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A comparison theorem for the planar strip isoperimetric problem",
  "title_text": "A comparison theorem for the planar strip isoperimetric problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/5907f8wxvd9ss",
  "venue": "arXiv",
  "versions": []
}