Extremal distance, harmonic measure and numerical conformal mapping
This is essentially a study on the crowding phenomenon in numerical conformal mapping which means that an arc \(E\) of the boundary of a simply connected domain \(G\) may be compressed exponentially by the map \(g\) from \(G\) to \(\mathbb{D}\) if \(G\) is a slender region. This can be made precise by the use of harmonic measure. A new aspect is the application of an estimate due to Pfluger in which the harmonic measure is estimated directly by geometric quantities like area and inner Euclidean distance.
scientific article; zbMATH DE number 219114
scientific article