Geodesic
Extremal sections of complex $l_{p}$-balls, $0 p \leq 2$
Alexander Koldobsky1 ; Marisa Zymonopoulou2
1Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
2Department of Mathematics University of Missouri-Columbia Columbia MO 65211, U.S.A.
Studia Mathematica, Tome 159 (2003) no. 2, pp. 185-194
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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.
DOI : 10.4064/sm159-2-2
Keywords: study extremal volume central hyperplane sections complex n dimensional p balls minimum corresponds hyperplanes orthogonal vectors mathinner ldotp ldotp ldotp mathbb mathinner ldotp ldotp ldotp maximum corresponds hyperplanes orthogonal vectors only non zero coordinate

Alexander Koldobsky  1   ; Marisa Zymonopoulou  2

1 Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
2 Department of Mathematics University of Missouri-Columbia Columbia MO 65211, U.S.A. 
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Alexander Koldobsky; Marisa Zymonopoulou. Extremal sections of complex $l_{p}$-balls, $0 < p \leq 2$. Studia Mathematica, Tome 159 (2003) no. 2, pp. 185-194. doi: 10.4064/sm159-2-2

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