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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 6, Pages 1298–1312
DOI: https://doi.org/10.33048/smzh.2021.62.607 (Mi smj7629) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Properties of minimal surfaces over depth 2 Carnot manifolds

M. B. Karmanova

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (364 kB) Citations (2)
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DOI: https://doi.org/10.33048/smzh.2021.62.607
Abstract: We derive necessary and sufficient conditions for the minimality of the graph surfaces for the classes of contact mappings of depth 2 Carnot manifolds into Carnot–Carathéodory spaces of the same depth. The basic case of the problem is for the mappings whose range is a nilpotent graded group. We describe some necessary and sufficient conditions for the well-posedness of this problem which are specific precisely to nonholonomic spaces without group structure that include requirements on the domain of definition.
Keywords: Carnot–Carathéodory space, Carnot manifold, graph mapping, nilpotent graded group, intrinsic measure, area functional, horizontal homomorphism, minimal surface, sub-Riemannian mean curvature.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0006
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0006).
Received: 16.11.2020
Revised: 02.08.2021
Accepted: 11.08.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 6, Pages 1050–1062
DOI: https://doi.org/10.1134/S0037446621060070
Bibliographic databases:
Document Type: Article
UDC: 517.518.1+517.2
MSC: 35R30
Language: Russian
Citation: M. B. Karmanova, “Properties of minimal surfaces over depth 2 Carnot manifolds”, Sibirsk. Mat. Zh., 62:6 (2021), 1298–1312; Siberian Math. J., 62:6 (2021), 1050–1062
Citation in format AMSBIB
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\paper Properties of minimal surfaces over depth~2 Carnot manifolds
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\pages 1298--1312
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\crossref{https://doi.org/10.33048/smzh.2021.62.607}
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\pages 1050--1062
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Linking options:
  • https://www.mathnet.ru/eng/smj7629
  • https://www.mathnet.ru/eng/smj/v62/i6/p1298
    • This publication is cited in the following 2 articles:
    1. M. B. Karmanova, “O minimalnykh poverkhnostyakh nad mnogoobraziyami Karno proizvolnoi glubiny”, Matem. tr., 25:1 (2022), 74–101  mathnet  crossref
    2. M. B. Karmanova, “Minimal Surfaces Over Carnot Manifolds”, Sib. Adv. Math., 32:3 (2022), 211  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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