Equilibrium measure

Summary

The equilibrium measure of a compact set $K$ is the way a unit charge distributes itself on $K$ when it minimizes its energy. In the plane the energy is the logarithmic energy, and in $\R^n$ with $n \ge 3$ it is the Newtonian energy. When $K$ has positive capacity, the minimizing measure exists and is unique. Its potential is constant on most of $K$, and this constant determines the capacity of the set.