ABSTRACT
One of the most beautiful results in classical complex analysis is the Riemann
mapping theorem. This result assures that the topological property "simply connected" is sufficient to describe, up to biholomorphisms, a large class of
plane domains. On the other hand, the Euclidean ball and the bidisc in <C2
are topologically equivalent to simply connected domains, but they are not
biholomorphic. This observation was made by H. Poincare. There are many other fundamental and interesting results in function theory of one complex variable that can not be extended to functions of several complex variables.
