Intrinsic Lipschitz Graphs in Heisenberg Groups

In the last few years there have been a fairly large amount of work dedicated to the study of intrinsic submanifolds of various dimension and codimension inside the Heisenberg groups H or more general Carnot groups. For example intrinsically C surfaces, rectifiable sets, finite perimeter sets, various notions of convex surfaces have been studied. Here and in what follows, intrinsic will denote properties defined only in terms of the group structure of H or, equivalently, of its Lie algebra h. We postpone complete definitions of H to the next section. Here we remind that H, with group operation ·, is a (connected and simply connected) Lie group identified through exponential coordinates with R. If h denotes the Lie algebra of all left invariant vector fields on