Extremal sections of complex $l_{p}$-balls, $0 < p \leq 2$
Volume 159 / 2003
Studia Mathematica 159 (2003), 185-194
MSC: 52A21, 46B07.
DOI: 10.4064/sm159-2-2
Abstract
We study the extremal volume of central hyperplane sections of complex $n$-dimensional $l_p$-balls with $0< p\le 2.$ We show that the minimum corresponds to hyperplanes orthogonal to vectors $\xi =(\xi ^1,\mathinner {\ldotp \ldotp \ldotp },\xi ^n)\in {{\mathbb C}}^n$ with $|\xi ^1|=\mathinner {\ldotp \ldotp \ldotp }=|\xi ^n|$, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.
