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Sibirsk. Mat. Zh., 2018, Volume 59, Number 4, Pages 834–857 (Mi smj3013)  

Three-dimensional graph surfaces on five-dimensional Carnot–Carathéodory spaces

M. B. Karmanova

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We study the class of codimension 2 graph surfaces over some three-dimensional Lie groups and establish some analogs of the differential properties of the corresponding graph mappings. Moreover, we derive the area formula and describe the classes of minimal surfaces of codimension 1 and 2.

Keywords: three-dimensional Lie group, three-dimensional Carnot-Carathéodory space, graph mapping, polynomial sub-Riemannian differentiability, area formula, minimal surface.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-31063 мол_а
The author was supported by the Russian Foundation for Basic Research (Grant 14-01-31063 mol_a).


DOI: https://doi.org/10.17377/smzh.2018.59.408

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English version:
Siberian Mathematical Journal, 2018, 59:4, 657–676

Bibliographic databases:

Document Type: Article
UDC: 517.2+517.4+514.7
MSC: 35R30
Received: 01.02.2016
Revised: 30.01.2018

Citation: M. B. Karmanova, “Three-dimensional graph surfaces on five-dimensional Carnot–Carathéodory spaces”, Sibirsk. Mat. Zh., 59:4 (2018), 834–857; Siberian Math. J., 59:4 (2018), 657–676

Citation in format AMSBIB
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\paper Three-dimensional graph surfaces on five-dimensional Carnot--Carath\'eodory spaces
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 4
\pages 834--857
\mathnet{http://mi.mathnet.ru/smj3013}
\crossref{https://doi.org/10.17377/smzh.2018.59.408}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 4
\pages 657--676
\crossref{https://doi.org/10.1134/S0037446618040080}
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