Common
Riemann mapping theorem
Mathematical theorem
Riemann mapping theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number plane C {\displaystyle \mathbb {C} } which is not all of C {\displaystyle \mathbb {C} } , then there exists a biholomorphic mapping f {\displaystyle f} (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U {\displaystyle U} onto the open unit disk D = { z ∈ C : | z | < 1 } . {\displaystyle D=\{z\in \mathbb {C} :|z|<1\}.} This mapping is sometimes called the...
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