On convex bodies with rotationally symmetric planar projections

Sergii Myroshnychenko; Dmitry Ryabogin; Christos Saroglou

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arXiv · 2609.27192

On convex bodies with rotationally symmetric planar projections

Sergii Myroshnychenko·Dmitry Ryabogin·Christos Saroglou

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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.

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BibTeX RIS

Sergii Myroshnychenko, Dmitry Ryabogin, Christos Saroglou. 2026-09-23. On convex bodies with rotationally symmetric planar projections. https://arxiv.org/abs/2609.27192

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