Stronger versions of the Orlicz-Petty projection inequality

TL;DR

This paper confirms a conjecture related to the Orlicz-Petty projection inequality, identifying the conditions for equality and establishing an almost optimal stability version, advancing understanding in convex geometric analysis.

Contribution

It verifies a conjecture on the equality case in the Orlicz-Petty projection inequality and provides an optimal stability result, enhancing theoretical understanding.

Findings

Confirmed the conjecture on equality cases

Established an essentially optimal stability version

Advances in convex geometric analysis

Abstract

We verify a conjecture of Lutwak, Yang, Zhang about the equality case in the Orlicz-Petty projection inequality, and provide an essentially optimal stability version.