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A solution to Sheil-Small's harmonic mapping problem for polygons


Authors: Daoud Bshouty, Erik Lundberg and Allen Weitsman
Journal: Proc. Amer. Math. Soc. 143 (2015), 5219-5225
MSC (2010): Primary 30C55; Secondary 31A05, 58E20
DOI: https://doi.org/10.1090/proc/12454
Published electronically: August 20, 2015
MathSciNet review: 3411139
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Abstract: The problem of mapping the interior of a Jordan polygon univalently by the Poisson integral of a step function was posed by T. Sheil-Small (1989). We describe a simple solution using ``ear clipping'' from computational geometry.


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Additional Information

Daoud Bshouty
Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel
Email: daoud@tx.technion.ac.il

Erik Lundberg
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida, 33431
Email: elundber@fau.edu

Allen Weitsman
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: weitsman@purdue.edu

DOI: https://doi.org/10.1090/proc/12454
Received by editor(s): December 12, 2012
Received by editor(s) in revised form: September 17, 2013, and January 20, 2014
Published electronically: August 20, 2015
Communicated by: Michael Wolf
Article copyright: © Copyright 2015 American Mathematical Society