One of the central results in the subject of complex analysis, the Riemann mapping theorem unifies the areas of algebra, geometry, and topology. Today it is recognized as one of the most important theorems of nineteenth-century mathematics, even though...

In complex analysis, the Riemann mapping theorem states that if U is a simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic (bijective and holomorphic) mapping...