On the volume of sections of a convex body by cones

Fradelizi, Matthieu; Meyer, Mathieu; Yaskin, Vlad

doi:10.1090/proc/13457

On the volume of sections of a convex body by cones
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by Matthieu Fradelizi, Mathieu Meyer and Vlad Yaskin PDF

Proc. Amer. Math. Soc. 145 (2017), 3153-3164 Request permission

Abstract:

We prove that in small codimensions, the sections of a convex body in $\mathbb R^n$ through its 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.

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