Abstract:
We derive necessary and sufficient conditions for the minimality of the graph surfaces for the classes of contact mappings of depth 2 Carnot manifolds into Carnot–Carathéodory spaces of the same depth. The basic case of the problem is for the mappings whose range is a nilpotent graded group. We describe some necessary and sufficient conditions for the well-posedness of this problem which are specific precisely to nonholonomic spaces without group structure that include requirements on the domain of definition.
Keywords:Carnot–Carathéodory space, Carnot manifold, graph mapping, nilpotent graded group, intrinsic measure, area functional, horizontal homomorphism, minimal surface, sub-Riemannian mean curvature.
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