Concave conformal mappings and pre-vertices of Schwarz-Christoffel mappings

Chuaqui, M.; Duren, P.; Osgood, B.

doi:10.1090/S0002-9939-2012-11455-8

Concave conformal mappings and pre-vertices of Schwarz-Christoffel mappings
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by M. Chuaqui, P. Duren and B. Osgood PDF

Proc. Amer. Math. Soc. 140 (2012), 3495-3505 Request permission

Abstract:

Normalized conformal mappings of the disk onto the exterior of a convex polygon are studied via a representation formula provided by Schwarz’s 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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