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arXiv · 0812.0053

On the total mean curvature of non-rigid surfaces

Victor Alexandrov
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Abstract

Using 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 and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.

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Victor Alexandrov. 2008-11-29. On the total mean curvature of non-rigid surfaces. https://doi.org/10.1007/s11202-009-0087-3

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