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Visual
representation of the Riemann and Ahlfors maps via the
Kerzman–Stein equation
Michael Bolt, Sarah Snoeyink and Ethan Van Andel |
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Vol. 3 (2010), No. 4, 405–420
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Abstract |
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The Szegő kernel serves as one of the canonical functions associated to a region in the complex plane, and from it one can compute the Riemann (or Ahlfors) map, the essentially unique conformal transformation of the region to the unit disc. We provide an elementary description of the method that Kerzman and Stein used to compute the Szegő kernel, and subsequently, the Riemann and Ahlfors maps. A description, too, is provided for a new tool that generates visual representations of these functions and is included with the open-source computer algebra system Sage. |
Keywords
Riemann map, Ahlfors map, Szegő kernel, Kerzman–Stein
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Mathematical Subject Classification 2000
Primary: 30C30
Secondary: 65E05
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Milestones
Received: 23 July 2010
Revised: 16 November 2010
Accepted: 20 November 2010
Published: 6 January 2011
Proposed: Michael Dorff
Communicated by Michael Dorff
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Authors |
| Michael Bolt | |
| Department of Mathematics and
Statistics Calvin College 3201 Burton St., S.E. Grand Rapids, MI 49546 United States |
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| http://www.calvin.edu/~mdb7/ | |
| Sarah Snoeyink | |
| Department of Mathematics University of Colorado at Boulder Campus Box 395 Boulder, CO 80309 United States |
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| Ethan Van Andel | |
| Department of Mathematics and
Statistics Calvin College 3201 Burton St., S.E. Grand Rapids, MI 49546 United States |
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| © 2010 MSP (Mathematical Sciences Publishers). |
