Centroids of sections of convex bodies and Lusternik-Schnirelmann category

Julian Haddad, C. Hugo Jiménez, Rafael Villa

Given two symmetric convex bodies $L\subseteq K\subseteq {\mathbb{R}}^n$ with $L$ strictly convex, we prove that there exist at least $n$ hyperplanes $H$ tangent to $L$, such that the cent…