Conformal Mapping
Möbius transformations, Schwarz–Christoffel, and the Riemann mapping theorem.
Conformal Mapping. Möbius transformations, Schwarz–Christoffel, and the Riemann mapping theorem. This page collects canonical references that organise the subject and provide entry points to its main techniques.
Foundations and canonical references
The standard treatments of conformal mapping approach the subject from complementary angles. Nehari, Conformal Mapping (1952) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Ahlfors, Complex Analysis (1979) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for conformal mapping include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1952Conformal Mappingnehari-1952
- textbook · primary · 1979Complex Analysisahlfors-1979
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