On the average volume of sections of convex bodies

2016/07/17 by Brazitikos, Silouanos, Dann, Susanna, Giannopoulos, Apostolos +1 · 1 citation
#52A20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1607.04862

Abstract

The average section functional \rm as(K) of a centered convex body in \mathbb Rⁿ is the average volume of central hyperplane sections of K: \rm as(K)=∫_S^n-1|K∩ ξ^⊥ | dσ(ξ). We study the question if there exists an absolute constant C>0 such that for every n, for every centered convex body K in \mathbb Rⁿ and for every 0

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