Extremal sections and projections of certain convex bodies: a survey

Abstract

We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly ${\ell }_p$ balls, by and onto lower dimensional subspaces. This subject emerged from geometry of numbers several decades ago and since then has seen development of a variety of probabilistic and analytic methods, showcased in this survey.

References updated. To appear in "Harmonic Analysis and Convexity"

Cited by in corpus (3)

• Stability of polydisc slicing
• Distributional stability of the Szarek and Ball inequalities
• Resilience of cube slicing in ${\ell }_p$