How far apart can the projection of the centroid of a convex body and the centroid of its projection be?

Sergii Myroshnychenko; Kateryna Tatarko; Vladyslav Yaskin

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arXiv · 2212.14456

How far apart can the projection of the centroid of a convex body and the centroid of its projection be?

Sergii Myroshnychenko·Kateryna Tatarko·Vladyslav Yaskin

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Abstract

We show that there is a constant $D \approx 0.2016$ such that for every $n$, every convex body $K\subset \mathbb R^n$, and every hyperplane $H\subset \mathbb R^n$, the distance between the projection of the centroid of $K$ onto $H$ and the centroid of the projection of $K$ onto $H$ is at most $D$ times the width of $K$ in the direction of the segment connecting the two points. The constant $D$ is asymptotically sharp.

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Sergii Myroshnychenko, Kateryna Tatarko, Vladyslav Yaskin. 2022-12-29. How far apart can the projection of the centroid of a convex body and the centroid of its projection be?. https://arxiv.org/abs/2212.14456

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