Geometric function theory: Difference between revisions

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Let <math>z_0</math> be a point in a simply-connected region <math>D_1 (D_1 \neq \mathbb{C})</math> and <math>D_1</math> having at least two boundary points. Then there exists a unique analytic function <math>w=f(z)</math> mapping <math>D_1</math> bijectively into the open unit disk <math>|w| < 1</math> such that <math>f(z_0)=0</math> and <math>f'(z_0) > 0</math>.

It should be noted that whileAlthough [[Riemann's mapping theorem]] demonstrates the existence of a mapping function, it does not actually ''exhibit'' this function. An example is given below.

[[File:Illustration of Riemann Mapping Theorem.JPG|Illustration of Riemann Mapping Theorem]]