I'm trying to learn the Pansu differentiability theorem and I need to know what Carnot groups are. Can someone please explain what Carnot groups are? An introductory reference would be greatly appreciated as well.


Thanks.



What are Carnot groups?
I learned the theory of Carnot group or more general subRiemannian manifolds from the thesis of Monti, which can be found here:
<http://www.math.unipd.it/~monti/PAPERS/TesiFinale.pdf>
In particular, Section 2 is devoted to the proof of Pansu-differentiability theorem.


Another good notes is by le donne, which [can be found here](https://65ac2831-a-62cb3a1a-s-sites.googlegroups.com/site/enricoledonne/LeDonne_subRiemannian.pdf)
. However the proof of Pansu differentiability theorem is stated without a proof.


By the way, the reference provided above "Gromov, Mikhael Carnot-Carathéodory spaces seen from within. Sub-Riemannian geometry, 79–323, Progr. Math., 144, Birkhäuser, Basel, 1996." is also a nice research suvery.


