A+ CATEGORY SCIENTIFIC UNIT

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

Volume 159 / 2003

Alexander Koldobsky, Marisa Zymonopoulou 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.

Authors

  • Alexander KoldobskyDepartment of Mathematics
    University of Missouri-Columbia
    Columbia, MO 65211, U.S.A.
    e-mail
  • Marisa ZymonopoulouDepartment of Mathematics
    University of Missouri-Columbia
    Columbia MO 65211, U.S.A.
    e-mail

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