turkmath.org

First we shall present some basic facts about logarithmic capacity, analytic capacity and Green function in the complex plane. Motivated by considerations related to the semi-additivity property of analytic capacity, we will study the lemniscates of good rational functions. We will prove a reflection principle for the harmonic measure of rational lemniscates and we will give estimates for their capacity and the capacity of their components. This is joint work with Thomas Ransford.