English

On star-convex bodies with rotationally invariant sections

Metric Geometry 2024-05-27 v4

Abstract

We will prove that an origin-symmetric star-convex body KK with sufficiently smooth boundary and such that every hyperplane section of KK passing through the origin is a body of affine revolution, is itself a body of affine revolution. This will give a positive answer to the recent question asked by G. Bor, L. Hern\'andez-Lamoneda, V. Jim\'enez de Santiago, and L. Montejano-Peimbert, though with slightly different prerequisites.

Keywords

Cite

@article{arxiv.2304.07074,
  title  = {On star-convex bodies with rotationally invariant sections},
  author = {Bartłomiej Zawalski},
  journal= {arXiv preprint arXiv:2304.07074},
  year   = {2024}
}

Comments

Beitr\"age zur Algebra und Geometrie (2023)

R2 v1 2026-06-28T10:05:55.669Z