On the volume of sections of a convex body by cones
  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. 
Matthieu Fradelizi, Mathieu Meyer, and Vlad Yaskin
math.MG math.FA