On minimal surfaces on two-step Carnot groups

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


About the authors

M. B. Karmanova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Author for correspondence.
Email: maryka@math.nsc.ru

Russian Federation, 4, Acad. Koptyug prospect, Novosibirsk, 630090


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Abstract - 194

PDF (Russian) - 96


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