# A direct proof of the Brunn-Minkowski inequality in Nilpotent Lie groups

## TL;DR

This paper provides a direct proof of the Brunn-Minkowski inequality within nilpotent Lie groups, extending classical Euclidean results to a more complex algebraic setting.

## Contribution

It introduces a novel direct proof method for the Brunn-Minkowski inequality in nilpotent Lie groups, based on classical Euclidean techniques.

## Key findings

- Established the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups
- Extended Euclidean inequality techniques to non-commutative groups
- Provided a new approach for inequalities in geometric analysis

## Abstract

The purpose of this work is to give a direct proof of the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann's one of the classical Brunn-Minkowski inequality in Euclidean space.