2 problems

Let $\Omega$ be a bounded domain, let $\Omega^*$ denote the comparison domain of the same area, and let $B_R$ be the comparison ball for a domain whose transfinite diameter is $R$.…

Asymptotic Faber–Krahn shape conjecture. After possibly translating the $G_n$, the Hausdorff distance between $G_n^*$ and $D$ converges to $0$ as $n\to\infty$.