Measures of sections of convex bodies

TL;DR

This survey reviews recent advances in slicing inequalities for convex bodies, emphasizing the extension from volume measures to arbitrary measures, highlighting new theoretical developments.

Contribution

It compiles and discusses recent results on slicing inequalities involving arbitrary measures, expanding the understanding beyond volume-based measures.

Findings

Recent results extend slicing inequalities to arbitrary measures.

New theoretical bounds have been established for convex bodies.

The survey highlights open problems and future research directions.

Abstract

This article is a survey of recent results on slicing inequalities for convex bodies. The focus is on the setting of arbitrary measures in place of volume.