Problem 1780 (difficulty: 6/10)

For all \(\displaystyle D \subset \CC\) domain and \(\displaystyle a \in D\) there is a unique \(\displaystyle r(a, D)\) radius such that there is a conformal injection \(\displaystyle f: D \leftrightarrow S\big(0, r(a, D)\big), \ f(a)=0, \ f'(a)=1\).

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