How far apart can the projection of the centroid of a convex body and the centroid of its projection be?
S Myroshnychenko, K Tatarko, V Yaskin - Mathematische Annalen, 2024 - Springer
S Myroshnychenko, K Tatarko, V Yaskin
Mathematische Annalen, 2024•SpringerWe show that there is a constant D≈ 0.2016 such that for every n, every convex body K⊂ R
n, and every hyperplane H⊂ 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.
n, and every hyperplane H⊂ 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.
Abstract
We show that there is a constant such that for every n, every convex body and every hyperplane 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.
Springer
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