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arXiv · 2402.12552

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

Jacek Jakimiuk·Hermann König
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Abstract

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

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Jacek Jakimiuk, Hermann König. 2024-02-19. Maximal sections of the unit ball of $l^n_p(\mathbb{C})$ for $p > 2$. https://arxiv.org/abs/2402.12552

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