On Sections of Convex Bodies in John's Position and of Generalised B_pⁿ Balls

2025/10/15 by Alonso-Gutiérrez, David, Brazitikos, Silouanos, Chasapis, Giorgos · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Primary 52A23 #Secondary 60D05

paper · doi:10.48550/arxiv.2510.14047

Abstract

We revisit an ingenious argument of K. Ball to provide sharp estimates for the volume of sections of a convex body in John's position. Our technique combines the geometric Brascamp-Lieb inequality with a generalised Parseval-type identity. This lets us complement some earlier results of the first two named authors, as well as generalise the classical estimates of Meyer-Pajor and Koldobsky regarding extremal sections of B_pⁿ balls to a broader family of norms induced by a John's decomposition of the identity in ℝⁿ.

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