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

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

Full text: PDF file (403 kB)
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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
\Bibitem{Kar18}
\by M.~B.~Karmanova
\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}
\elib{https://elibrary.ru/item.asp?id=35723252}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 4
\pages 657--676
\crossref{https://doi.org/10.1134/S0037446618040080}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000443717700008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85053000292}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. B. Karmanova, “On the class of Hölder surfaces in Carnot–Carathéodory spaces”, Siberian Math. J., 60:5 (2019), 861–885  mathnet  crossref  crossref  isi  elib
    2. M. B. Karmanova, “On minimal surfaces on two-step Carnot groups”, Dokl. Math., 99:2 (2019), 185–188  crossref  crossref  zmath  isi  elib  scopus
    		• Сибирский математический журнал Siberian Mathematical Journal
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