Conformal Mapping of Multiply Connected Domains

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

Chapter Chapter V in Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, 1950, pp 167-198 from Springer

Abstract: Abstract Objective. In Chapters I and II, the conformal mapping of general Riemann domains G on slit domains B was obtained by employing Dirichlet’s Principle to construct functions in G mapping G onto B. A different approachl to the problem of conformal mapping of arbitrary domains G on individuals of any of three classes ℜ of normal domains B is provided by the methods of Chapters III and IV; Dirichlet’s Principle is used there to construct functions in B giving the inverse mapping of B onto G. Restricting ourselves to k-fold connected plane domains G,2 we shall pursue this latter approach to obtain a variety of mapping theorems stating that arbitrary3k-fold connected domains can be mapped conformally onto individuals of a great variety of specific classes ℜ of domains.

Keywords: Unit Circle; Branch Point; Conformal Mapping; Boundary Curve; Jordan Curve (search for similar items in EconPapers)
Date: 1950
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DOI: 10.1007/978-1-4612-9917-2_6

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