On Minimal Surfaces on Two-Step Carnot Groups

Abstract

For graph mappings constructed from contact mappings of arbitrary two-step Carnot groups, conditions for the correct formulation of the minimal surfaces problem are found. A suitable notion of the increment of the (sub-Riemannian) area functional is introduced, the differentiability of this functional is proved, and necessary minimality conditions for graph surfaces are deduced. These conditions are also expressed in terms of the sub-Riemannian mean curvature.