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May 2021 Weinstock inequality in higher dimensions
Dorin Bucur, Vincenzo Ferone, Carlo Nitsch, Cristina Trombetti
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J. Differential Geom. 118(1): 1-21 (May 2021). DOI: 10.4310/jdg/1620272940

Abstract

We prove that the Weinstock inequality for the first nonzero Steklov eigenvalue holds in $\mathbb{R}^n$, for $n \geq 3$, in the class of convex sets with prescribed surface area. The key result is a sharp isoperimetric inequality involving simultaneously 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. "Weinstock inequality in higher dimensions." J. Differential Geom. 118 (1) 1 - 21, May 2021. https://doi.org/10.4310/jdg/1620272940

Information

Received: 13 October 2017; Published: May 2021
First available in Project Euclid: 7 May 2021

Digital Object Identifier: 10.4310/jdg/1620272940

Subjects:
Primary: 35J05 , 35P15 , 47J30

Keywords: inverse mean curvature flow , Stekloff Laplacian eigenvalues , Weinstock , Wentzell

Rights: Copyright © 2021 Lehigh University

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Vol.118 • No. 1 • May 2021
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