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.

中文翻译：

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卡诺组中的多指数映射及其在凸性和可微性上的应用

我们分析了在卡诺（Carnot）组的几何分析中自然出现的一类多指数映射的某些属性。我们将看到，这样的映射至少可以在两个有趣的问题中有用：首先，关于水平凸集的某些规律性分析。然后，我们将证明我们的多指数图可用于证明从固定点到subRiemannian距离的Pansu可微性。