On subspace concentration for dual curvature measures

TL;DR

This paper investigates how dual curvature measures of certain convex bodies concentrate in subspaces, providing bounds that unify and extend known symmetric case results using divergence theorem techniques.

Contribution

It introduces upper bounds on subspace concentration for dual curvature measures of convex bodies with specific symmetry, generalizing previous symmetric results.

Findings

Upper bounds depend on parameter γ

Unified proof approach via divergence theorem

Extends symmetric case results to asymmetric bodies

Abstract

We study subspace concentration of dual curvature measures of convex bodies $K$ satisfying $\gamma (-K)\subseteq K$ for some $\gamma \in (0,1]$. We present upper bounds on the subspace concentration depending on $\gamma$, which, in particular, retrieves the known results in the symmetric setting. The proof is based on a unified approach to prove necessary subspace concentration conditions via the divergence theorem.