Infinitesimal rigidity of smooth convex surfaces through the second derivative of the Hilbert-Einstein functional
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 respect to...