Difference between revisions of "Riemann Mapping Theorem"
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| − | '''Riemann mapping theorem''' states that if U is a simply connected, open, proper subset of the complex plane, then there exist a unique | + | '''Riemann mapping theorem''' states that if ''U'' is a simply connected, open, proper subset of the complex plane and x<sub>0</sub> is a point in ''U'', then there exist a unique function ''f'' mapping U to the interior of the [[unit disc]] such that ''f(x<sub>0</sub>) = 0'' and ''f'(x<sub>0</sub>) > 0''. |
[[category:complex analysis]] | [[category:complex analysis]] | ||
Revision as of 01:56, April 20, 2007
Riemann mapping theorem states that if U is a simply connected, open, proper subset of the complex plane and x0 is a point in U, then there exist a unique function f mapping U to the interior of the unit disc such that f(x0) = 0 and f'(x0) > 0.