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

 Messages: [ Previous | Next ]
 Dr. Eric Wingler Posts: 139 Registered: 12/12/04
Re: Riemann mapping theorem
Posted: Mar 24, 2006 11:39 AM

"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
330-941-1817

Date Subject Author
3/24/06 Lara
3/24/06 Dr. Eric Wingler
3/24/06 jirka@5z.com
3/25/06 David C. Ullrich