Stability of the log-Brunn-Minkowski inequality in the case of many hyperplane symmetries

TL;DR

This paper proves a stability version of the log-Brunn-Minkowski and Minkowski inequalities for convex bodies with symmetries across multiple hyperplanes, advancing understanding of geometric inequalities under symmetry constraints.

Contribution

It introduces a stability result for these inequalities specifically in the context of convex bodies symmetric with respect to many hyperplanes, a novel extension in geometric analysis.

Findings

Established stability of the inequalities under hyperplane symmetries

Extended the inequalities to convex bodies with multiple symmetries

Provided new bounds and conditions for equality cases

Abstract

In the case of symmetries with respect to n independent linear hyperplanes, a stability version of the logarithmic Brunn-Minkowski inequality and the logarithmic Minkowski inequality for convex bodies is established.