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arXiv · 2208.03221

Reflections of convex bodies and their sections

Jorge L. Arocha·Javier Bracho·Luis Montejano
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Abstract

The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the case of a non-spherical ellipsoid, where a surprising structure arises (Section 2). These results allow us to give a new characterization of ellipsoids in terms of their reflections and, on the other hand, to prove a result deeply related to a conjecture due to K. Bezdek.

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Jorge L. Arocha, Javier Bracho, Luis Montejano. 2022-08-05. Reflections of convex bodies and their sections. https://arxiv.org/abs/2208.03221

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