On the total mean curvature of non-rigid surfaces
Differential Geometry
2009-10-10 v1 Metric Geometry
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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Cite
@article{arxiv.0812.0053,
title = {On the total mean curvature of non-rigid surfaces},
author = {Victor Alexandrov},
journal= {arXiv preprint arXiv:0812.0053},
year = {2009}
}
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4 pages