{
  "abstract": "For planar convex bodies $A_0,A_1,A_2$ satisfying $\\frac12(A_0+A_2)\\subseteq A_1$, we prove that the union of the three slices $\\{i\\}\\times A_i\\subseteq\\mathbb{R}^3$, $i=0,1,2$, contains a point such that every closed halfspace containing it captures at least $2/9$ of their total area. This establishes the three-slice case of Oertel's mixed-integer centerpoint conjecture in $\\mathbb{Z}\\times\\mathbb{R}^2$ with the best possible constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32953",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongyu Cheng"
    },
    {
      "name": "Amitabh Basu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57nj121rdyaer.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32953",
  "fulltext_url": null,
  "id": "57nj121rdyaer",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32953",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7214762821",
  "pdf_url": "https://arxiv.org/pdf/2609.32953",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57nj121rdyaer.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32953",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32953"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A centerpoint theorem for three planar convex bodies",
  "title_text": "A centerpoint theorem for three planar convex bodies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/57nj121rdyaer",
  "venue": "arXiv",
  "versions": []
}