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On the volume of sections of a convex body by cones
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math.MGmath.FA
keywords
convexbodysectionsvolumeanswerbodiescentroidcodimensions
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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.
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