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arXiv · 1910.11638

Locating diametral points

Jin-ichi Itoh·Costin Vîlcu·Liping Yuan·Tudor Zamfirescu
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Abstract

Let $K$ be a convex body in $\mathbb{R} ^d$, with $d = 2,3$. We determine sharp sufficient conditions for a set $E$ composed of $1$, $2$, or $3$ points of ${\rm bd}K$, to contain at least one endpoint of a diameter of $K$ (for $d=2,3$). We extend this also to convex surfaces, with their intrinsic metric. Our conditions are upper bounds on the sum of the complete angles at the points in $E$. We also show that such criteria do not exist for $n\geq 4$ points.

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Jin-ichi Itoh, Costin Vîlcu, Liping Yuan, Tudor Zamfirescu. 2019-10-25. Locating diametral points. https://arxiv.org/abs/1910.11638

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