= Solution
{c}
The <Riemann mapping theorem> gives a <conformal bijection> $G\to D$ exactly when
$$
\boxed{G\ne\mathbb C,}
$$
given the hypothesis that $G$ is a <simply connected domain>. A <domain> is nonempty, <open>, and <connected>, so no extra nonemptiness qualification is needed.
For necessity, a <conformal bijection> $\mathbb C\to D$ would be a bounded nonconstant <entire function>, contradicting the <Liouville theorem>. For sufficiency, $G$ is a proper <simply connected domain>, exactly the hypothesis of the <Riemann mapping theorem>.
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