Comparing volumes by concurrent cross-sections of complex lines: a Busemann-Petty type problem

We consider the problem of comparing the volumes of two star bodies in an even-dimensional euclidean space \mathbb R^{2n} = \mathbb C^n by comparing their cross sectional areas along complex lines (special 2-dimensional real planes) through the origin. Under mild symmetry conditions on one of the bodies a Busemann-Petty type... Show more