Stability of volume comparison for complex convex bodies

We prove stability in the affirmative part of the Busemann-Petty problem on sections of complex convex bodies

Stability and separation in volume comparison problems

We review recent stability and separation results in volume comparison problems and use them to prove several hyper- plane inequalities for intersection and projection bodies.Comment: arXiv admin note: text overlap with arXiv:1101.3600, arXiv:1204.253