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Normalized conformal mappings of the disk onto the exterior of a convex polygon are studied via a representation formula provided by Schwarzâs lemma. Some conditions on the pre-vertices for corresponding Schwarz- Christoffel mappings are obtained. There is a connection to finite Blaschke products that characterizes the pre-vertices and leads to a curious property of Blaschke products themselves.
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Chuaqui et al. (2012) studied this question.
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