Graphs of bounded variation, existence and local boundedness of non-parametric minimal surfaces in Heisenberg groups

Abstract In the setting of the sub-Riemannian Heisenberg group ℍ n , we introduce and study the classes of t - and intrinsic graphs of bounded variation. For both notions we prove the existence of non-parametric area-minimizing surfaces, i.e., of graphs with the least possible area among those with the same boundary. For minimal graphs we also prove a local boundedness result which is sharp at least in the case of t -graphs in ℍ 1 .