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Mat. Tr., 2010, Volume 13, Number 2, Pages 3–9 (Mi mt197)  

This article is cited in 2 scientific papers (total in 2 papers)

On constant mean curvature surfaces in the Heisenberg group

D. A. Berdinskyab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: This work is devoted to the theory of surfaces of constant mean curvature in the three-dimensional Heisenberg group. It is proved that each surface of such a kind locally corresponds to some solution of the system of a sine-Gordon type equation and a first order partial differential equation.

Key words: Heisenberg group, constant mean curvature surface.

Full text: PDF file (157 kB)
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English version:
Siberian Advances in Mathematics, 2012, 22:2, 75–79

Bibliographic databases:

Document Type: Article
UDC: 514.772.22
Received: 09.04.2010

Citation: D. A. Berdinsky, “On constant mean curvature surfaces in the Heisenberg group”, Mat. Tr., 13:2 (2010), 3–9; Siberian Adv. Math., 22:2 (2012), 75–79

Citation in format AMSBIB
\Bibitem{Ber10}
\by D.~A.~Berdinsky
\paper On constant mean curvature surfaces in the Heisenberg group
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 2
\pages 3--9
\mathnet{http://mi.mathnet.ru/mt197}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2789954}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 2
\pages 75--79
\crossref{https://doi.org/10.3103/S1055134412020010}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Berdinskii D.A., “O minimalnykh poverkhnostyakh v gruppe geizenberga”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 34–38  mathscinet  elib
    2. Dorfmeister J.F., Inoguchi J.-I., Kobayashi Sh., “a Loop Group Method For Minimal Surfaces in the Three-Dimensional Heisenberg Group”, Asian J. Math., 20:3 (2016), 409–448  crossref  mathscinet  zmath  isi  scopus
  • Математические труды Siberian Advances in Mathematics
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