Pólya–Szegő conjecture on the logarithmic-to-Newtonian capacity ratio

Let $K\subset\mathbb R^2$ be compact. The logarithmic capacity $\operatorname{Cap}_0(K)$ and Newtonian capacity $\operatorname{Cap}_1(K)$ are the corresponding Riesz capacities. Pólya–Szegő's conjecture.

$$\operatorname{Cap}_1(K)\leq \frac{2}{\pi}\operatorname{Cap}_0(K).$$

Equivalently, the disk should retain more of its logarithmic capacity than any other planar set when passing to Newtonian capacity; the conjecture is unresolved.