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Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 3, Pages 496–511 (Mi smj43)  
This article is cited in 4 scientific papers (total in 4 papers)

Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

D. A. Berdinskii, I. A. Taimanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (241 kB) Citations (4)
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Abstract: We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem.
Keywords: Heisenberg group, surface of revolution, isoperimetric problem, Willmore functional.
Received: 13.10.2006
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 3, Pages 395–407
DOI: https://doi.org/10.1007/s11202-007-0043-z
Bibliographic databases:
UDC: 514.772.22
Language: Russian
Citation: D. A. Berdinskii, I. A. Taimanov, “Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional”, Sibirsk. Mat. Zh., 48:3 (2007), 496–511; Siberian Math. J., 48:3 (2007), 395–407
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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