Siberian Mathematical Journal

, 50:757 | Cite as

On the total mean curvature of a nonrigid surface

  • Victor A. Alexandrov


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.


infinitesimal flex vector field flux of a vector field circulation of a vector field Green’s formula 


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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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