{
  "abstract": "For a convex body $K$ its parallel section function in the direction $θ\\in S^{n-1}$ is defined by $$A_{K,θ}(t) = \\mathrm{vol}_{n-1} \\left( K \\cap \\{ x \\in \\mathbb{R}^n ~ | ~ \\langle x, θ\\rangle = t \\} \\right) .$$ We study to what extent the body $K$ is determined by partial information about these functions. As applications, we characterize convex bodies with locally separable section functions, establish partial results on the homothety conjecture for bodies of flotation, and answer a question of Barker and Larman concerning the determination of convex bodies from section functions at infinitely many distances from the origin.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10229",
  "author_total": 4,
  "authors": [
    {
      "name": "Alexander Fish"
    },
    {
      "name": "Dmitry Ryabogin"
    },
    {
      "name": "Wen Rui Sun"
    },
    {
      "name": "Vladyslav Yaskin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pd6vb2zrs5rg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10229",
  "fulltext_url": null,
  "id": "1pd6vb2zrs5rg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10229",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7220949598",
  "pdf_url": "https://arxiv.org/pdf/2610.10229",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pd6vb2zrs5rg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10229",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10229"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On determination of convex bodies by their section functions",
  "title_text": "On determination of convex bodies by their section functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/1pd6vb2zrs5rg",
  "venue": "arXiv",
  "versions": []
}