Abstract
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.
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The author was supported by the Russian Foundation for Basic Research (Grant 17–01–00875).
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Karmanova, M.B. Classes of Maximal Surfaces on Carnot Groups. Sib Math J 61, 803–817 (2020). https://doi.org/10.1134/S0037446620050043
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DOI: https://doi.org/10.1134/S0037446620050043
Keywords
- Carnot group
- contact mapping
- intrinsic measure
- area formula
- sub-Lorentzian area functional
- maximal surface