Conformal Mapping on Parallel-Slit Domains

Richard Courant
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Richard Courant: New York University, Institute for Mathematics and Mechanics

Chapter Chapter II in Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, 1950, pp 45-93 from Springer

Abstract: Abstract Classes of Normal Domains. Parallel-Slit Domains. As shown in Chapter I, every simply connected domain G in the plane (except the full plane or the plane with one point removed) can be mapped conformally on the unit circle; every doubly connected domain G (except the plane with two points removed) can be mapped onto a circular ring whose outer circle may be chosen as the unit circle, the inner circle depending on G and possibly degenerating to a point.

Keywords: Conformal Mapping; Plane Domain; Admissible Function; Genus Zero; Klein Bottle (search for similar items in EconPapers)
Date: 1950
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DOI: 10.1007/978-1-4612-9917-2_3

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