Geometric function theory: Difference between revisions

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Revision as of 18:40, 29 October 2011

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==Riemann mapping theorem==

Let ''z''{{su|b=0}} be a point in a simply-connected region ''D''{{su|b=1}} (''D''{{su|b=1}}≠ ℂ) and ''D''{{su|b=1}} having at least two boundary points. Then there exists a unique analytic function ''w = f(z)'' mapping ''D''{{su|b=1}} bijectively into the open unit disk |''w''|<1 such that ''f(''z''{{su|b=0}})''=0 and

''Re f ′(''z''{{su|b=0}})''=>0.

It should be noted that while [[Riemann's mapping theorem]] demonstrates the existence of a mapping function, it does not actually ''exhibit'' this function.