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Weinstock inequality in higher dimensions
Journal of Differential Geometry ( IF 1.3 ) Pub Date : 2021-05-01 , DOI: 10.4310/jdg/1620272940
Dorin Bucur 1 , Vincenzo Ferone 2 , Carlo Nitsch 2 , Cristina Trombetti 2
Affiliation  

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:

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
更新日期:2021-05-01
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