Author:
Lai Duc Nam,Huang Qingzhong,He Binwu
Abstract
Abstract
The problem of maximal hyperplane section of
B
p
(
C
n
)
with
p
≥
1
is considered, which is the complex version of central hyperplane section problem of
B
p
(
R
n
)
. The relation between the complex slicing problem and the complex isotropic constant of a body is established, an upper bound estimate for the volume of complex central hyperplane sections of normalized complex
ℓ
p
(
C
n
)
-balls that does not depend on n and p is shown, which extends results of Oleszkiewicz and Pełczyński, Koldobsky and Zymonopoulou, and Meyer and Pajor.
MSC:52A21, 46B07.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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