The Riemann Mapping Theorem

Peter V. Dovbush and Steven G. Krantz
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Peter V. Dovbush: Moldova State University, Institute of Mathematics and Computer Science
Steven G. Krantz: Washington University in St. Louis, Mathematics, CB 1146

Chapter Chapter 2 in The Geometric Theory of Complex Variables, 2025, pp 5-34 from Springer

Abstract: Abstract We are interested in the following question: Given a domain in the complex plane, can we find a conformal map from this domain onto some simple domain? This is the uniformization problem in its simplest form. The first result in this direction is the famous Riemann mapping theorem that states that any simply connected planar domain can be conformally mapped onto the complex plane ℂ $$\mathbb {C}$$ or the unit disc 𝔻 $$\mathbb {D}$$ .

Date: 2025
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DOI: 10.1007/978-3-031-77204-7_2

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