Estimates for the extremal sections of complex lp-balls

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 Pelczynski, Koldobsky and Zymonopoulou, and Meyer and Pajor.