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arXiv · 2510.14047

On Sections of Convex Bodies in John's Position and of Generalised $B_p^n$ Balls

David Alonso-Gutiérrez·Silouanos Brazitikos·Giorgos Chasapis
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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 $B_p^n$ balls to a broader family of norms induced by a John's decomposition of the identity in $\mathbb{R}^n$.

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David Alonso-Gutiérrez, Silouanos Brazitikos, Giorgos Chasapis. 2025-10-15. On Sections of Convex Bodies in John's Position and of Generalised $B_p^n$ Balls. https://arxiv.org/abs/2510.14047

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