On the total mean curvature of non-rigid surfaces

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.

💡 Research Summary

The paper investigates the variation of the total mean curvature of a smooth closed surface S in Euclidean three‑space. The total mean curvature is defined as
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