# Geometric Hardy inequalities on starshaped sets

## TL;DR

This paper establishes geometric Hardy inequalities on starshaped sets within Carnot groups and extends these inequalities to half-spaces for general vector fields, broadening the scope of Hardy inequality applications.

## Contribution

It introduces new geometric Hardy inequalities on starshaped sets in Carnot groups and generalizes these inequalities to half-spaces with arbitrary vector fields.

## Key findings

- Hardy inequalities derived for starshaped sets in Carnot groups
- Extension of Hardy inequalities to half-spaces with general vector fields
- Broadened applicability of Hardy inequalities in geometric analysis

## Abstract

In this paper, we present the geometric Hardy inequalities on the starshaped sets in the Carnot groups. Also, we obtain the geometric Hardy inequalities on half-spaces for general vector fields.