  We prove that the Weinstock inequality for the first nonzero Steklov
eigenvalue holds in $\mathbb{R}^n$, for $n\ge 3$, in the class of convex sets
with prescribed surface area. The key result is a sharp isoperimetric
inequality involving simultanously the surface area, the volume and the
boundary momentum of convex sets. As a by product, we also obtain some
isoperimetric inequalities for the first Wentzell eigenvalue

Analysis of PDEs