On a certain property of a transformation in Hilbert space in connection with the theory of differential equations
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The paper is centered around a new proof of the infinitesimal rigidity of smooth closed surfaces with everywhere positive Gauss curvature. We use a reformulation that replaces deformation of an embedding by deformation of the metric inside the body bounded by the surface. The proof is obtained by studying derivatives of the Hilbert-Einstein functional with boundary term. This approach is in a sense dual to proving Gauss infinitesimal rigidity, that is, rigidity with...
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