The affine subspace concentration inequality for centered convex bodies

TL;DR

This paper establishes an affine subspace concentration inequality for centered convex bodies, extending previous results from polytopes to a broader class of convex bodies, advancing the understanding of geometric concentration phenomena.

Contribution

It introduces an affine version of the subspace concentration inequality applicable to centered convex bodies, generalizing prior polytope-specific results.

Findings

Proves the affine subspace concentration inequality for convex bodies.

Extends previous polytope results to all centered convex bodies.

Provides a new tool for geometric analysis of convex bodies.

Abstract

An affine version of the linear subspace concentration inequality as proposed by Wu is established for centered convex bodies. This generalizes results from Wu and Freyer, Henk, Kipp on polytopes to convex bodies.