On the volume of sections of a convex body by cones

Abstract

Let $K$ be a convex body in ${\mathbb{R}}^n$. We prove that in small codimensions, the sections of a convex body through the centroid are quite symmetric with respect to volume. As a consequence of our estimates we give a positive answer to a problem posed by M. Meyer and S. Reisner regarding convex intersection bodies.

arXiv comment13 pages