A solution to Sheil-Small’s harmonic mapping problem for polygons
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- by Daoud Bshouty, Erik Lundberg and Allen Weitsman PDF
- Proc. Amer. Math. Soc. 143 (2015), 5219-5225 Request permission
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.References
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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
- MR Author ID: 819273
- Email: elundber@fau.edu
- Allen Weitsman
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- Email: weitsman@purdue.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5219-5225
- MSC (2010): Primary 30C55; Secondary 31A05, 58E20
- DOI: https://doi.org/10.1090/proc/12454
- MathSciNet review: 3411139