Bell representations of finitely connected planar domains

In this paper, we solve a conjecture of S. Bell (1992) affirmatively. Actually, we prove that every non-degenerate $n$-connected planar domain $\Omega$, where $n>1$is representable as $\Omega= \{\vert f\vert<1\}$with a suitable rational function $f$of degree $n$. This result is considered as a natural generalization of the classical Riemann mapping theorem for simply connected planar domains.