Schwarz–Christoffel mapping

In complex analysis, a Schwarz–Christoffel mapping is a conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon. Such a map is guaranteed to exist by the Riemann mapping theorem (stated by Bernhard Riemann in 1851); the Schwarz–Christoffel formula provides an explicit construction. They were introduced independently by Elwin Christoffel in 1867 and Hermann Schwarz in 1869.

Schwarz–Christoffel mappings are used in potential theory and some of its applications, including minimal surfaces, hyperbolic art, and fluid dynamics.