Robin constant

Summary

The Robin constant of a compact set $K$ in the plane is the least logarithmic energy of a unit charge placed on $K$. It is a number in $(-\infty, \infty]$, and it equals $\infty$ exactly when every unit charge on $K$ has infinite energy. The logarithmic capacity of $K$ is $e^{-V}$, where $V$ is the Robin constant. The Robin constant also appears in the expansion at infinity of the Green function of the outside of $K$.