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 with sufficiently smooth boundary and such that every hyperplane section of 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)