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Maximal sections of the unit ball of $\ell ^n_p(\mathbb C)$ for $p \gt 2$

Volume 283 / 2025

Jacek Jakimiuk, Hermann König Studia Mathematica 283 (2025), 177-201 MSC: Primary 52A38; Secondary 52A40, 46B07, 60F05 DOI: 10.4064/sm240526-12-3 Published online: 4 July 2025

Abstract

Eskenazis, Nayar and Tkocz (2024) showed some resilience of Ball’s celebrated cube slicing theorem, namely its analogue in $\ell^n_p$ for large $p$. We show that the complex analogue, i.e. resilience of the polydisc slicing theorem proven by Oleszkiewicz and Pełczyński (2000), holds for large $p$ and small $n$, but does not hold for any $p \gt 2$ and large $n$.

Authors

  • Jacek JakimiukInstitute of Mathematics
    University of Warsaw
    02-097 Warszawa, Poland
    e-mail
  • Hermann KönigMathematisches Seminar
    Universität Kiel
    24098 Kiel, Germany
    e-mail

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