Raul Paolo Serapioni
Università di Trento, Trento, Italy

A natural class of regular surfaces inside a Carnot group $\mathbb G$ are the non critical level sets of horizontal $\mathcal{C}^1$ functions $\mathbb{G}\to \mathbb{R}^k$. These surfaces can be locally characterized as graphs of uniformly intrinsic differentiable functions acting between complementary subgroups of $\mathbb G$.

In turn, for a large class of step $2$ groups, uniformly intrinsic differentiable functions can be characterized as functions with continuous intrinsic derivatives. Here intrinsic derivatives are non linear first order differential operators depending on the structure of the ambient group $\mathbb G$.

These results extend the ones obtained by Luigi Ambrosio, Francesco Serra Cassano and Davide Vittone inside Heisenberg groups.