Maximal sections of the unit ball of lⁿ_p(ℂ) for p > 2

2024/02/19 by Jacek Jakimiuk, Jakimiuk, Jacek, Hermann König +1
Mathematics · #46 B07 #52A38 #52A40 (Primary) #60F05 (Secondary) #Analytic Number Theory Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2402.12552

openalex publication_date 2024/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Eskenazis, Nayar and Tkocz have shown recently some resilience of Ball's celebrated cube slicing theorem, namely its analogue in lⁿ_p 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.

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