How could one prove that among the biholomorphic functions that map a fixed simply-connected open domain $D$ into open subsets of $\mathbb{C}$, there is such a biholomorphic map $f$ for each open simply-connected $U\subset\mathbb{C}$, such that $f(D)=U$? Also I would like to avoid the use of Riemann mapping theorem in such a proof.
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closed as not a real question by Andres Caicedo, jvp, Bill Johnson, David Roberts, Qiaochu Yuan Jul 16 2011 at 4:48 |
