Sur l'ensemble critique d'un ensemble convexe. (On the critical set of a convex set)
Define the critical set of a convex body K in a finite dimensional Euclidean space as follows: for point \(p\in K\), \(\lambda (p)= \max \{\lambda \geq 0,\quad (1+\lambda)p-\lambda K\subseteq K\},\quad \lambda (K)= \max_{p\in K} \lambda (p),\) and \(C(K)=\{q\in K: \lambda (q)=\lambda (K)\}\). C(K) is called the critical set of K. The author shows that every convex body in \({\mathbb{R}}^ n\) is the critical set of some convex body in \({\mathbb{R}}^{n+2}\).
scientific article; zbMATH DE number 4028286