A generalization of Gr\"unbaum's inequality
Metric Geometry
2024-10-11 v1
Abstract
Gr\"unbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of this inequality for hyperplanes that do not necessarily contain the centroid. As an application, we obtain a sharp inequality that compares sections of a convex body to the maximal section parallel to it.
Cite
@article{arxiv.2410.04741,
title = {A generalization of Gr\"unbaum's inequality},
author = {Brayden Letwin and Vladyslav Yaskin},
journal= {arXiv preprint arXiv:2410.04741},
year = {2024}
}