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arXiv · 1710.04587

Weinstock inequality in higher dimensions

Dorin Bucur·Vincenzo Ferone·Carlo Nitsch·Cristina Trombetti
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Abstract

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

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Dorin Bucur, Vincenzo Ferone, Carlo Nitsch, Cristina Trombetti. 2017-10-13. Weinstock inequality in higher dimensions. https://arxiv.org/abs/1710.04587

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