Complex Lp-intersection bodies

Interpolating between the classical notions of intersection and polar centroid bodies, (real) L-p-intersection bodies, for -1 < p < 1, play an important role in the dual L-p-Brunn-Minkowski theory. Inspired by the recent construction of complex centroid bodies, a complex version of L-p-intersection bodies, with range extended to p >-2, is introduced, interpolating between complex intersection and polar complex centroid bodies. It is shown that the complex L-p-intersection body of an S-1-invariant convex body is pseudoconvex, if -2 < p <-1and convex, if p >=-1. Moreover, intersection inequalities of Busemann-Petty type in the sense of Adamczak-Paouris-Pivovarov-Simanjuntak are deduced. (c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).