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Sibirsk. Mat. Zh., 2009, Volume 50, Number 5, Pages 963–966 (Mi smj2023)  

This article is cited in 6 scientific papers (total in 6 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

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.

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English version:
Siberian Mathematical Journal, 2009, 50:5, 757–759

Bibliographic databases:

UDC: 514.772
Received: 11.02.2009

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

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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. Dowdall R.J., Gomes H., Hellmann F., “Asymptotic analysis of the Ponzano–Regge model for handlebodies”, J. Phys. A, 43:11 (2010), 115203, 27 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Velimirović L.S., Ćirić M.S., Cvetković M.D., “Change of the Willmore energy under infinitesimal bending of membranes”, Comput. Math. Appl., 59:12 (2010), 3679–3686  crossref  mathscinet  zmath  isi  scopus
    3. Velimirovic L.S., Ciric M.S., Velimirovic N.M., “On the Willmore energy of shells under infinitesimal deformations”, Computers & Mathematics with Applications, 61:11 (2011), 3181–3190  crossref  mathscinet  zmath  isi  scopus
    4. Velimirovic L.S., Ciric M.S., “On the total mean curvature of piecewise smooth surfaces under infinitesimal bending”, Appl Math Lett, 24:9 (2011), 1515–1519  crossref  mathscinet  zmath  isi  scopus
    5. I. Kh. Sabitov, “Isometric surfaces with a common mean curvature and the problem of Bonnet pairs”, Sb. Math., 203:1 (2012), 111–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. M. V. Neshchadim, “The mean integral curvature and infinitesimal deformations of a surface in a three-dimensional Riemannian space”, Siberian Math. J., 55:5 (2014), 954–960  mathnet  crossref  mathscinet  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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