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This article is cited in 2 scientific papers (total in 2 papers)
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.
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:
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
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\pages 834--857
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\jour Siberian Math. J.
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\vol 59
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\pages 657--676
\crossref{https://doi.org/10.1134/S0037446618040080}
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Linking options:
http://mi.mathnet.ru/eng/smj3013 http://mi.mathnet.ru/eng/smj/v59/i4/p834
Citing articles on Google Scholar:
Russian citations,
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Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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M. B. Karmanova, “On the class of Hölder surfaces in Carnot–Carathéodory spaces”, Siberian Math. J., 60:5 (2019), 861–885
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M. B. Karmanova, “On minimal surfaces on two-step Carnot groups”, Dokl. Math., 99:2 (2019), 185–188
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