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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 5, Pages 963–966 (Mi smj2023)  
This article is cited in 9 scientific papers (total in 9 papers)

On the total mean curvature of a nonrigid surface

V. A. Alexandrov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (262 kB) Citations (9)
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Abstract: Using the Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field, which immediately yields the following well-known theorem: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.
Keywords: infinitesimal flex, vector field, flux of a vector field, circulation of a vector field, Green's formula.
Received: 11.02.2009
English version:
Siberian Mathematical Journal, 2009, Volume 50, Issue 5, Pages 757–759
DOI: https://doi.org/10.1007/s11202-009-0087-3
Bibliographic databases:
UDC: 514.772
Language: Russian
Citation: V. A. Alexandrov, “On the total mean curvature of a nonrigid surface”, Sibirsk. Mat. Zh., 50:5 (2009), 963–966; Siberian Math. J., 50:5 (2009), 757–759
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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