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On minimal surfaces on two-step Carnot groups
- Authors: Karmanova M.B.1
-
Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
- Issue: Vol 485, No 4 (2019)
- Pages: 410-414
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/13541
- DOI: https://doi.org/10.31857/S0869-56524854410-414
- ID: 13541
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Abstract
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
References
- Karmanova M., Vodopyanov S. Geometry of Carnot-Carathéodory Spaces, Differentiability, Coarea and Area Formulas. In: Analysis and Mathematical Phy-sics. Basel: Birkhäuser, 2009. P. 233-335.
- Карманова М. Б. Минимальные поверхности-графики на произвольных двуступенчатых группах Карно // Изв. вузов. Математика. 2019.
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- Карманова М.Б. // Сиб. мат. журн. 2017. Т. 58. № 2. С. 232-254.
- Vodopyanov S. // Contemp. Math. 2007. V. 424. P. 247-301.
- Карманова М.Б. // Сиб. мат. журн. 2018. Т. 59. № 4. С. 834-857.
- Карманова М.Б. // ДАН. 2018. Т. 480. № 1. С. 16-20.
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