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.References
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Additional Information
- M. Chuaqui
- Affiliation: Facultad de Matemáticas, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
- MR Author ID: 319580
- Email: mchuaqui@mat.puc.cl
- P. Duren
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1043
- Email: duren@umich.edu
- B. Osgood
- Affiliation: Department of Electrical Engineering, Stanford University, Stanford, California 94305-9510
- MR Author ID: 134465
- Email: osgood@stanford.edu
- 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
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 3495-3505
- MSC (2010): Primary 30C55; Secondary 30J10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11455-8
- MathSciNet review: 2929018