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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