Geodesic
On conformal maps from multiply connected domains onto lemniscatic domains
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 1-15
We study conformal maps from multiply connected domains in the extended complex plane onto lemniscatic domains. Walsh proved the existence of such maps in 1956 and thus obtained a direct generalization of the Riemann mapping theorem to multiply connected domains. For certain polynomial preimages of simply connected sets, we derive a construction principle for Walsh's conformal map in terms of the Riemann map for the simply connected set. Moreover, we explicitly construct examples of Walsh's conformal map for certain radial slit domains and circular domains.
Classification : 30C35, 30C20
Keywords: conformal mapping, multiply connected domains, lemniscatic domains 
@article{ETNA_2016__45__a25,
     author = {S\`ete,  Olivier and Liesen,  J\"org},
     title = {On conformal maps from multiply connected domains onto lemniscatic domains},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--15},
     year = {2016},
     volume = {45},
     zbl = {1345.30010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2016__45__a25/}
}
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%A Liesen,  Jörg
%T On conformal maps from multiply connected domains onto lemniscatic domains
%J Electronic transactions on numerical analysis
%D 2016
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%F ETNA_2016__45__a25
Sète,  Olivier; Liesen,  Jörg. On conformal maps from multiply connected domains onto lemniscatic domains. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 1-15. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a25/