---
abstract: 'We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann’s theorem to the complex case by proving that complex intersection bodies of symmetric complex convex bodies are also convex. Other results include stability in the complex Busemann-Petty problem for arbitrary measures and the corresponding hyperplane inequality for measures of complex intersection bodies.'
address:
- |
    Department of Mathematics\
    University of Missouri\
    Columbia\
    Missouri 65211
- |
    Department of Mathematics\
    Texas A $\&$ M University\
    College Station\
    TX 77843- 3368\
- |
     Department of Mathematics\
    University of Crete\
    Heraklio\
    Crete
author:
- 'A. Koldobsky'
- 'G. Paouris'
- 'M. Zymonopoulou'
title: Complex intersection bodies
---

\[section\] \[theorem\][Lemma]{} \[theorem\][Proposition]{} \[theorem\][Corollary]{} Ł[[L]{}]{} [[F]{}]{}[[F]{}]{} |[c]{} v ł

Introduction
============

The concept of an intersection body was introduced by Lutwak [@L], as part of his dual Brunn-Minkowski theory. In particular, these bodies played an important role in the solution of the Busemann-Petty problem. Many results on intersection bodies have appeared in recent years (see [@G; @K1; @KY] and references there), but almost all of them apply to the real case. The goal of this paper is to extend 