Classes of maximal surfaces on carnot groups

Under study are the graph mappings constructed from the contact mappings of arbitrary Carnot groups. We establish the well-posedness conditions for the problem of maximal surfaces, introduce a suitable notion of the increment of the (sub-Lorentzian) area functional, and prove that this functional is differentiable. The necessary maximality conditions for graph surfaces are described in terms of the area functional as well as in terms of sub-Lorentzian mean curvature.