Logarithmic capacity

Summary

The logarithmic capacity of a compact set $K$ in the plane measures how large $K$ is from the point of view of potential theory. It is defined from the least possible logarithmic energy of a unit charge distributed on $K$. A disc of radius $r$ has capacity $r$, and a line segment of length $L$ has capacity $L/4$. Sets of capacity zero, the polar sets, are negligible for many questions on harmonic and holomorphic functions. Examples are removable singularities and the solvability of the Dirichlet problem.