Dérivation des surfaces convexes de $\QTR{Bbb}{R}^{3}$ dans l'espace de Lorentz et é}tude de leurs focales
Abstract
Introducing an appropriate notion of derivative of closed convex surfaces of $\QTR{Bbb}{R}^{3}$ in the Lorentz-Minkowski space $\QTR{Bbb}{R}^{3,1}$, we give a natutal three-dimensional equivalent of an upper bound of the isoperimetric deficit in terms of the signed area of the evolute of a closed convex curve of $\QTR{Bbb}{R}^{2}$. Furthermore we etablish a series of geometric inequalities for focals of closed convex surfaces.
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