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arXiv · 2410.04741

A generalization of Gr\"unbaum's inequality

Brayden Letwin·Vladyslav Yaskin
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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.

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Brayden Letwin, Vladyslav Yaskin. 2024-10-07. A generalization of Gr\"unbaum's inequality. https://arxiv.org/abs/2410.04741

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