In this paper, the properties of the maps for the Heisenberg group targets are studied. For u ∈ W^1，α (Ω, H^m), some Poincaré type inequalities are proved. For the energymini mizers, the e-regularity theorems and the singularity theorems are obtained.
The aim of this paper is to get the decomposition of distributional derivativesof functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose theapproximate continuity of BV functions is discussed first, then approximate differentialsof L1 functions are defined in the case that vector fields are of Carnot type and finally thedecomposition Xu = △u @ Ln + Xsu is proved, where u ∈ BVx(Ω) and △u denotes theapproximate differential of u.
