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Extremal sections of complex $l_{p}$ -balls, 0 < p ≤ 2

Alexander Koldobsky; Marisa Zymonopoulou — 2003

Studia Mathematica

We study the extremal volume of central hyperplane sections of complex n-dimensional $l_{p}$ -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.

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Extremal sections of complex l p -balls, 0 < p ≤ 2

Extremal sections of complex $l_{p}$ -balls, 0 < p ≤ 2