2 problems

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Reverse Faber–Krahn conjecture for the logarithmic potential operator
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 $R$ .…
Conjectureopenfaber-krahn potential-theory spectral-geometryarXiv posted 2 days ago
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The asymptotic Faber–Krahn shape conjecture for subgraphs of the integer lattice
Asymptotic Faber–Krahn shape conjecture. After possibly translating the $G_n$ , the Hausdorff distance between $G_n^*$ and $D$ converges to $0$ as $n\to\infty$ .
Conjectureopendiscrete-laplacian faber-krahn spectral-geometryarXiv posted 2 days ago

Reverse Faber–Krahn conjecture for the logarithmic potential operator