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 } .
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 } .
Source: Wikipedia "Riemann mapping theorem" · CC BY-SA 4.0
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