Do Minkowski averages get progressively more convex?

Matthieu Fradelizi, Mokshay Madiman, Arnaud Marsiglietti +1

Let us define, for a compact set $A\subset {\mathbb{R}}^n$, the Minkowski averages of $A$: $$ A(k) = \left\{\frac{a_1+\cdots +a_k}{k} : a_1, \ldots, a_k\in A\right\}=\frac{1}{k}\Big…