On the structure of finite perimeter sets in step 2 Carnot groups

Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group

“…Remark. From Definition 2.10 and Lemma 2.12 we immediately deduce that |∂E| H −a.e p ∈ H n belongs to the reduced boundary ∂ * H E. We end this section with a collection of results that are the Heisenberg counterpart of the BV function theory in the Euclidean space, see [11], [23] and [24].…”

“…A notable class of intrinsic C 1 and Lipschitz surfaces has been identified by means of their invariance with respect to the sub-Riemannian structure. They have been defined in the framework of rectifiable sets (see, for instance, [2,3,15,23,24,26,29,32,35,40]), with several applications to geometry of Banach spaces, theoretical computer science, mathematical models in neurosciences (see, for instance, [12,17,19,30,42]). We refer the reader to the monograph [11] and the references therein for a more detailed introduction to the Heisenberg group and the afore-mentioned arguments.…”

“…Sets of intrinsic finite perimeter in H n . In this subsection we will recall some useful concepts of geometric measure theory in H n , see [23], [24], [27], [11] and reference therein.…”

An intrinsic measure for submanifolds in stratified groups

“…Here we address the reader to some relevant papers [1], [2], [5], [4], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [21], [25], [26], [28], [29], [22], [23], [30], [31], [33], [34], [36], [37], [39], [43], [44], [45], [46] and the reference therein.…”

“…Recall that horizontal points of hypersurfaces coincide with the well known characteristic points, that play an important role in the study of hypersurfaces in stratified groups, [5], [9], [14], [15], [18], [20], [22], [23], [34], [38], [40].…”