On Schwarz-Christoffel Mappings

Martin Chuaqui; Christian Pommerenke

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arXiv · 1207.6143

On Schwarz-Christoffel Mappings

Martin Chuaqui·Christian Pommerenke

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Abstract

We extend previous work on Schwarz-Chrsitoffel mappings, including the special cases when the image is a convex polygon or its complement. We center our analysis on the relationship between the pre-Schwrazian of such mappings and Blaschke products. For arbitrary Schwarz-Christoffel mappings, we resolve an open question in \cite{ChDO2} that relates the degrees of the associated Blaschke products with the number of convex and concave vertices of the polygon. In addition, we obtain a sharp sufficient condition in terms of the exterior angles for the injectivity of a mapping given by the Schwarz-Christoffel formula, and study the geometric interplay between the location of the zeros of the Blaschke products and the separation of the pre-vertices.

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Martin Chuaqui, Christian Pommerenke. 2014-05-22. On Schwarz-Christoffel Mappings. https://arxiv.org/abs/1207.6143

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