Extremal distance, harmonic measure and numerical conformal mapping

AbstractDeLillo, T.K. and J.A. Pfaltzgraff, Extremal distance, harmonic measure and numerical conformal mapping, Journal of Computational and Applied Mathematics 46 (1993) 103–113.Estimates of extremal distance and harmonic measure are used to show how the geometric properties of a simply connected domain influence the boundary distortion of a conformal map from the unit disk to the domain. Numerical examples and remarks on the conditioning of numerical conformal mapping methods are included. A sharp estimate is given of the exponential ill-conditioning, known as the crowding phenomenon, which occurs for slender regions