Centroid of a convex body can be rarely the centroid of its sections

Abstract: We construct a convex body $K$ in $R^n$, $n \ge 5$, with the property that there is exactly one hyperplane $H$ passing through $c(K)$, the centroid of $K$, such that the centroid of $K \cap H$ coincides with $c(K)$. This provides answers to questions of Grunbaum and Loewner for $n \ge 5$. The proof is based on the existence of non-intersection bodies in these dimensions. Joint work with K. Tatarko and V. Yaskin.

Mathematics

Audience: researchers in the topic

PIMS-CORDS SFU Operations Research Seminar