Abstract
We consider Gauss rigidity and Gauss infinitesimal rigidity for hedgehogs of \({\mathbb{R}^{3}}\) (regarded as Minkowski differences of closed convex surfaces of \({\mathbb{R}^{3}}\) with positive Gaussian curvature). Besides, we prove under an appropriate differentiability condition that whenever we perform a deformation of a hedgehog so that its curvature function remains constant, its algebraic volume also remains constant.
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Martinez-Maure, Y. Gauss Rigidity and Volume Preservation Under Preserving Curvature Deformations for Hedgehogs. Results. Math. 63, 973–983 (2013). https://doi.org/10.1007/s00025-012-0248-8
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DOI: https://doi.org/10.1007/s00025-012-0248-8