Derivation of convex surfaces of \(\mathbb R^3\) in Lorentz space and study of their focals (Q616741)

Introducing a notion of derivation of closed convex surfaces of \(\mathbb R^3\) in the Lorentz-Minkowski space \(\mathbb R^{3,1}\), the author gives a natural three-dimensional equivalent of an upper bound of the isoperimetric deficit of convex curves of \(\mathbb R^2\) in terms of signed area of their evolute and establishes a series of geometric inequalities of Brunn-Minkowski type for focals of closed convex surfaces.