Area of intrinsic graphs and coarea formula in Carnot Groups

We consider submanifolds of sub-Riemannian Carnot groups with intrinsic $C^1$ regularity ($C_H^1$). Our first main result is an area formula for $C_H^1$ intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing $C_H^1$ submanifolds into level sets of a $C_H^1$ function.