On the volume of sections of a convex body by cones

Abstract : We prove that in small codimensions, the sections of a convex body in 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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Matthieu Fradelizi, Mathieu Meyer, Vlad Yaskin. On the volume of sections of a convex body by cones. Proceedings of the American Mathematical Society, American Mathematical Society, 2017, 145, pp.3153 - 3164. ⟨10.1090/proc/13457⟩. ⟨hal-01590236⟩

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