Polydisc slicing in $ℂ^n$
Studia Mathematica, Tome 142 (2000) no. 3, pp. 281-294
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
Let D be the unit disc in the complex plane ℂ. Then for every complex linear subspace H in $ℂ^n$ of codimension 1, $vol_{2n-2}(D^{n-1}) ≤ vol_{2n-2}(H ∩ D^{n}) ≤ 2vol_{2n-2}(D^{n-1})$. The lower bound is attained if and only if H is orthogonal to the versor $e_{j}$ of the jth coordinate axis for some j = 1,...,n; the upper bound is attained if and only if H is orthogonal to a vector $e_{j} + σe_{k}$ for some 1 ≤ j k ≤ n and some σ ∈ ℂ with |σ| = 1. We identify $ℂ^n$ with $ℝ^{2n}$; by $vol_{k}(·)$ we denote the usual k-dimensional volume in $ℝ^{2n}$. The result is a complex counterpart of Ball's [B1] result for cube slicing.
@article{10_4064_sm_142_3_281_294,
author = {Krzysztof Oleszkiewicz and Aleksander Pe{\l}czy\'nski},
title = {Polydisc slicing in $\ensuremath{\mathbb{C}}^n$},
journal = {Studia Mathematica},
pages = {281--294},
year = {2000},
volume = {142},
number = {3},
doi = {10.4064/sm-142-3-281-294},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-142-3-281-294/}
}
TY - JOUR AU - Krzysztof Oleszkiewicz AU - Aleksander Pełczyński TI - Polydisc slicing in $ℂ^n$ JO - Studia Mathematica PY - 2000 SP - 281 EP - 294 VL - 142 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-142-3-281-294/ DO - 10.4064/sm-142-3-281-294 LA - en ID - 10_4064_sm_142_3_281_294 ER -
Krzysztof Oleszkiewicz; Aleksander Pełczyński. Polydisc slicing in $ℂ^n$. Studia Mathematica, Tome 142 (2000) no. 3, pp. 281-294. doi: 10.4064/sm-142-3-281-294
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