# Dimensional transport inequalities and Brascamp-Lieb inequalities

## TL;DR

This paper explores new transport inequalities for convex measures, deriving dimensional Brascamp-Lieb inequalities and providing quantitative forms involving Wasserstein distances.

## Contribution

It introduces novel dimensional transport inequalities for convex measures and extends Brascamp-Lieb inequalities with quantitative Wasserstein-based forms.

## Key findings

- Derived new dimensional forms of Brascamp-Lieb inequalities.
- Established quantitative transport inequalities involving Wasserstein distances.
- Enhanced understanding of convex measure inequalities.

## Abstract

The goal of the present paper is to discuss new transport inequalities for convex measures. We retrieve some dimensional forms of Brascamp-Lieb inequalities. We also give some quantitative forms involving the Wasserstein's distances.