On conformal maps from multiply connected domains onto lemniscatic domains
Abstract
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 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2015
 arXiv:
 arXiv:1501.01812
 Bibcode:
 2015arXiv150101812S
 Keywords:

 Mathematics  Complex Variables;
 30C35;
 30C20
 EPrint:
 Added a remark for a generalization of Theorem 4.2