Let 
be a point in a simply connected region 
, where 
is the complex plane. Then
there is a unique analytic function 
mapping 
one-to-one onto the disk 
such that 
and 
. The corollary guarantees
that any two simply connected regions except
(the Euclidean plane) can be mapped conformally
onto each other.
Riemann Mapping Theorem
See also
Conformal MappingExplore with Wolfram|Alpha
References
Krantz, S. G. "The Riemann Mapping Theorem." §6.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 86-87, 1999.Referenced on Wolfram|Alpha
Riemann Mapping TheoremCite this as:
Weisstein, Eric W. "Riemann Mapping Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RiemannMappingTheorem.html