On the volume of sections of a convex body by cones

2016/04/12 by Fradelizi, Matthieu, Meyer, Mathieu, Yaskin, Vlad · 1 citation
#52A20 #52A40 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1604.05351

Abstract

Let K be a convex body in \mathbb Rⁿ. 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.

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