Convex-domain Robin maximisation conjecture

Let $\Omega\subset\mathbb{R}^d$ be a convex domain of fixed volume, and let $\lambda_1^\alpha(\Omega)$ be the first eigenvalue of the Robin problem with $\alpha<0$. Convex-domain Robin maximisation conjecture. The ball maximises $\lambda_1^\alpha(\Omega)$ among all such domains. The source explores convex domains numerically and presents this as a conjecture without a resolution.