We study the extremal volume of central hyperplane sections of complex n-dimensional -balls with 0 < p ≤ 2. We show that the minimum corresponds to hyperplanes orthogonal to vectors ξ = (ξ¹,...,ξⁿ) ∈ ℂⁿ with |ξ¹| = ... = |ξⁿ|, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-2,
author = {Alexander Koldobsky and Marisa Zymonopoulou},
title = {Extremal sections of complex $l\_{p}$-balls, 0 < p $\leq$ 2},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {185-194},
zbl = {1053.52005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-2}
}
Alexander Koldobsky; Marisa Zymonopoulou. Extremal sections of complex $l_{p}$-balls, 0 < p ≤ 2. Studia Mathematica, Tome 157 (2003) pp. 185-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-2/