External Angles and Hubbard Trees

Abstract

It is well known that analytic functions f:ℂ→ℂ are a powerful tool for solving problems of two-dimensional electrostatics. The Cauchy-Riemann differential equations imply that Ref and Imf are both solutions to Laplace’s equation ∇²F= 0, and that the two families of curves Ref= const and Imf= const intersect each other orthogonally. Therefore, if u=Ref say, describes the surface of a charged conductor, the lines Ref= const are equipotential lines and Imf= const the corresponding field lines.