# Multiexponential maps in Carnot groups with applications to convexity and differentiability

## TL;DR

This paper investigates multiexponential maps in Carnot groups, demonstrating their utility in analyzing convexity and proving Pansu differentiability of subRiemannian distances, advancing geometric analysis in subRiemannian geometry.

## Contribution

It introduces and analyzes multiexponential maps in Carnot groups, applying them to convexity and differentiability problems in subRiemannian geometry.

## Key findings

- Multiexponential maps help analyze regularity of horizontally convex sets.
- They can be used to prove Pansu differentiability of subRiemannian distances.
- The maps provide new tools for geometric analysis in Carnot groups.

## Abstract

We analyze some properties of a class of multiexponential maps appearing naturally in the geometric analysis of Carnot groups. We will see that such maps can be useful in at least two interesting problems. First, in relation to the analysis of some regularity properties of horizontally convex sets. Then, we will show that our multiexponential maps can be used to prove the Pansu differentiability of the subRiemannian distance from a fixed point.