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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 | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. B. Bhowmik, S. Ponnusamy, and K.-J. Wirths, Concave functions, Blaschke products, and polygonal mappings, Siberian Math. J. 50 (2009), 609-615. MR 2583615 (2011a:30123)
  • 2. M. Chuaqui, P. Duren, and B. Osgood, Schwarzian derivatives of convex mappings, Ann. Acad. Sci. Fenn. Math. 36 (2011), 449-460.
  • 3. S.-A. Kim and D. Minda, The hyperbolic and quasihyperbolic metrics in convex regions,
    J. Analysis 1 (1993), 109-118. MR 1230512 (94h:30005)
  • 4. A.I. Markushevich, Theory of Functions of a Complex Variable, Vol. 3, Prentice Hall, Englewood Cliffs, NJ, 1967. MR 0215964 (35:6799)
  • 5. B. Osgood, R. Phillips, and P. Sarnak, Compact sets of isospectral surfaces, J. Funct. Analysis 80 (1988), 212-234. MR 960229 (90d:58160)

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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

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