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Topic: Riemann mapping theorem
Replies: 3   Last Post: Mar 25, 2006 6:45 AM

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Dr. Eric Wingler

Posts: 139
Registered: 12/12/04
Re: Riemann mapping theorem
Posted: Mar 24, 2006 11:39 AM
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"Lara" <the_brat_taz@yahoo.com> wrote in message
> Show that for every conformal f: { z = x + iy , y >0} --->{ z = x + iy
> , y > 0}
> there exist a,b,c,d in R such that ad - bc = 1, f(z)= (az-b) / (cz-d)
> should we use Riemann mapping theorem ??

You shouldn't need anything as powerful as the Riemann mapping theorem.
Find two fractional linear transformations g and h such that go(foh) maps
the unit disc into the unit disc and such that g(f(h(0))) = 0.

Eric J. Wingler (wingler@math.ysu.edu)
Dept. of Mathematics and Statistics
Youngstown State University
One University Plaza
Youngstown, OH 44555-0001

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