Article
Computing Conformal Maps of Finitely Connected Domains onto Canonical Slit Domains
Theory of Computing Systems
(2012)
Abstract
We continue the research initiated in Andreev et al. (Computing conformal maps onto circular domains, 2010, submitted) on the computability of conformal mappings of multiply connected domains by showing that the conformal maps of a finitely connected domain onto the canonical slit domains can be computed uniformly from the domain and its boundary. Along the way, we demonstrate the computability of finding analytic extensions of harmonic functions and solutions to Neuman problems. These results on conformal mapping then follow easily from M. Schiffer’s constructions (Dirichlet Principle, Conformal Mapping and Minimal Surfaces, Interscience, New York, 1950).
Keywords
- Computable analysis,
- Conformal mapping
Disciplines
Publication Date
2012
DOI
10.1007/s00224-010-9305-4
Publisher Statement
The final publication is available at Springer via https://doi.org/10.1007/s00224-010-9305-4.
Copyright Springer Science+Business Media, LLC 2010.
Citation Information
Timothy H. McNicholl and Valentin V. Andreev. "Computing Conformal Maps of Finitely Connected Domains onto Canonical Slit Domains" Theory of Computing Systems Vol. 50 Iss. 2 (2012) p. 354 - 369 Available at: http://works.bepress.com/timothy-mcnicholl/6/