Open mapping theorem
which takes values in D. Thus by Liouville’s theorem, ˚ fis constant. ˚is invertible, so fis also constant. Spring 2009, 3. Find an explicit conformal equivalence which maps the open set bounded by z 1 2 i = 1 2 and jz ij= 1 onto the upper half plane U. I am too lazy to learn drawing circles in LaTeX now, so the reader should draw them. Let ...
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