Maximal sections of the unit ball of $l_p^n(\mathbb{C})$ for $p>2$

Abstract

Eskenazis, Nayar and Tkocz have shown recently some resilience of Ball's celebrated cube slicing theorem, namely its analogue in $l_p^n$ for large $p$. We show that the complex analogue, i.e. resilience of the polydisc slicing theorem proven by Oleszkiewicz and Pelczyński, holds for large $p$ and small $n$, but does not hold for any $p>2$ and large $n$.