  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.
