Email this article On Minimal Surfaces on Two-Step Carnot Groups
- Authors: Karmanova M.B.1
-
Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences
- Issue: Vol 99, No 2 (2019)
- Pages: 185-188
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225654
- DOI: https://doi.org/10.1134/S106456241902025X
- ID: 225654
Cite item
Open Access
Access granted
Subscription Access
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.
About the authors
M. B. Karmanova
Sobolev Institute of Mathematics, Siberian Branch,Russian Academy of Sciences
Author for correspondence.
Email: maryka@math.nsc.ru
Russian Federation, Novosibirsk, 630090
Supplementary files
