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The problem of maximal hyperplane section of Bp(Cn) with p≥1 is considered, which is the complex version of central hyperplane section problem of Bp(Rn). 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 ℓp(Cn)-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.

Estimates for the extremal sections of complex "Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML" -balls