I know the conformal automorphisms of the upper half plane are mobius transforms but I am stuck on using this to prove this statement. Any help would be appreciated.
2026-03-27 03:49:50.1774583390
Why is every conformal automorphism of the first complex quadrant a Mobius Transform?
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It is not. You get things like $\sqrt{z^2+1}$.
However, it is true that every conformal automorphism can be written as $\sqrt{F(z^2)}$ where $F$ is a conformal automorphism of the upper half plane.