Quantitative Borell-Brascamp-Lieb inequalities for compactly supported power concave functions (and some applications)

TL;DR

This paper enhances Borell-Brascamp-Lieb inequalities for compactly supported power concave functions, providing quantitative versions of classical geometric inequalities with applications to Brunn-Minkowski and Urysohn inequalities.

Contribution

It introduces strengthened, quantitative Borell-Brascamp-Lieb inequalities specifically for power concave functions with compact support, advancing the understanding of geometric inequalities.

Findings

Quantitative versions of Brunn-Minkowski inequality

Quantitative versions of Urysohn inequality for torsional rigidity

Enhanced Borell-Brascamp-Lieb inequalities for specific function classes

Abstract

We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski inequality and of the Urysohn inequality for torsional rigidity.