{
  "abstract": "Let $n\\ge 3$ and let $K\\subset\\mathbb R^n$ be a convex body. For a two-dimensional linear subspace $P\\subset\\mathbb R^n$, let $K|P$ be the orthogonal projection of $K$ onto $P$. We prove that if for every two-dimensional subspace $P$, the planar convex body $K|P$ has $q$-fold rotational symmetry up to translation, then for $q\\ge4$, this forces $K$ to be an Euclidean ball. The case $q=3$ is exceptional: non-spherical examples exist.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27192",
  "author_total": 3,
  "authors": [
    {
      "name": "Sergii Myroshnychenko"
    },
    {
      "name": "Dmitry Ryabogin"
    },
    {
      "name": "Christos Saroglou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5dnfybaqc9pfp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27192",
  "fulltext_url": null,
  "id": "5dnfybaqc9pfp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27192",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7214209882",
  "pdf_url": "https://arxiv.org/pdf/2609.27192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5dnfybaqc9pfp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27192"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On convex bodies with rotationally symmetric planar projections",
  "title_text": "On convex bodies with rotationally symmetric planar projections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/5dnfybaqc9pfp",
  "venue": "arXiv",
  "versions": []
}