Partitions and functional Santalo inequalities

TL;DR

This paper presents a new proof of the Blaschke-Santalo inequality by combining a logarithmic Prekopa-Leindler inequality with a partition theorem, offering a more direct approach to the functional Santalo inequality.

Contribution

It provides a novel, direct proof of the functional Santalo inequality, enhancing understanding of the Blaschke-Santalo inequality through innovative methods.

Findings

New direct proof of the functional Santalo inequality

Connection between Prekopa-Leindler inequality and partition theorems

Simplified proof of the Blaschke-Santalo inequality

Abstract

We give a direct proof of a functional Santalo inequality due to Fradelizi and Meyer. This provides a new proof of the Blaschke-Santalo inequality. The argument combines a logarithmic form of the Prekopa-Leindler inequality and a partition theorem of Yao and Yao.