  A Carnot group G is a connected, simply connected, nilpotent Lie group with
stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the
same role as C^1 surfaces in Euclidean spaces. As in Euclidean spaces,
intrinsic regular surfaces can be locally defined in different ways: e.g. as
non critical level sets or as continuously intrinsic differentiable graphs. The
equivalence of these natural definitions is the problem that we are studying.
Precisely our aim is to generalize some results proved by Ambrosio, Serra
Cassano, Vittone valid in Heisenberg groups to the more general setting of
Carnot groups.
