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

中文翻译：

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更高维度的温斯托克不等式

我们证明了第一个非零 Steklov 特征值的 Weinstock 不等式在 $\mathbb{R}^n$ 中成立，对于 $n\ge 3$，在具有规定表面积的凸集类中。关键结果是一个尖锐的等周不等式，同时涉及凸集的表面积、体积和边界动量。作为副产品，我们还获得了第一个 Wentzell 特征值的一些等周不等式