Surface-area Robin maximisation conjecture

Let $\Omega\subset\mathbb{R}^d$ be a domain with prescribed surface area, and let $\lambda_1^\alpha(\Omega)$ be the first eigenvalue of the Robin problem with $\alpha<0$. Surface-area Robin maximisation conjecture. The ball maximises $\lambda_1^\alpha(\Omega)$ among all domains of equal surface area. The claim is proposed as an extension of the paper's perimeter theorem to every dimension, and the source gives no proof of the extension.