PreprintCC BY 4.0arXiv
The dimension-free threshold for maximal sections of ℓp
Abstract
We prove the existence of a sharp threshold p0 ≈ 26.265…, such that for every n∈ℕ and p≥ p0, the volume maximizing section of the unit ball of ℓpn is the section with Ball's hyperplane ((e1+e2)/√2)⊥, whereas for p∈(2,p0) the asymptotic maximizer as the ambient dimension n→∞ is the hyperplane orthogonal to the diagonal vector (e1+⋯+en)/√n.
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BibTeX
@misc{brazitikos2026dimensionfree,
title = {{The dimension-free threshold for maximal sections of $\ell_p$}},
author = {Silouanos Brazitikos and Alexandros Eskenazis},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07619},
eprint = {2611.07619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07619},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The dimension-free threshold for maximal sections of ℓ_p
AU - Silouanos Brazitikos
AU - Alexandros Eskenazis
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07619
UR - https://arxiv.org/abs/2611.07619
AB - We prove the existence of a sharp threshold p_0 ≈ 26.265…, such that for every n∈ℕ and p≥ p_0, the volume maximizing section of the unit ball of ℓ_p^n is the section with Ball's hyperplane ((e_1+e_2)/√2)^⊥, whereas for p∈(2,p_0) the asymptotic maximizer as the ambient dimension n→∞ is the hyperplane orthogonal to the diagonal vector (e_1+⋯+e_n)/√n.
ER -