The local logarithmic Brunn-Minkowski inequality for zonoids

TL;DR

This paper proves that the local logarithmic Brunn-Minkowski inequality holds for zonoids, using a variant of the Bochner method, advancing understanding of convex geometric inequalities.

Contribution

It establishes the local form of the logarithmic Brunn-Minkowski conjecture specifically for zonoids, employing a novel adaptation of the Bochner technique.

Findings

The local logarithmic Brunn-Minkowski inequality is valid for zonoids.

A variant of the Bochner method can be effectively applied in convex geometry.

The proof provides new insights into the structure of zonoids and related inequalities.

Abstract

The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the Bochner method due to Shenfeld and the author.