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

Authors: M. Chuaqui, P. Duren and B. Osgood
Journal: Proc. Amer. Math. Soc. 140 (2012), 3495-3505
MSC (2010): Primary 30C55; Secondary 30J10
Published electronically: February 22, 2012
MathSciNet review: 2929018
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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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Additional Information

M. Chuaqui
Affiliation: Facultad de Matemáticas, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile

P. Duren
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1043

B. Osgood
Affiliation: Department of Electrical Engineering, Stanford University, Stanford, California 94305-9510

Received by editor(s): April 8, 2011
Published electronically: February 22, 2012
Additional Notes: The authors were supported in part by FONDECYT Grant #1110321.
Communicated by: Mario Bonk
Article copyright: © Copyright 2012 American Mathematical Society