The conformal mapping theorem of Riemann asserts that a simply connected domain in C, different from C, is biholomorphically equivalent to the open unit disc U = {z ∈C : |z| < 1}. Many authors have been interested in the generalization of this result in several complex variables (cf. [2; 3; 4; 9; 14]). The situation is quite different there: a small C~2 perturbation of the unit ball B~(n+1) in C~(n+1) can be nonequivalent to B~(n+1), even if it is simply connected. This shows that a domain in C~(n+1) is not completely described by its topological properties. Thus one must study the automorphism group of a domain to find a polynomial representation of it, that is, a rigid polynomial domain and a biholomorphic equivalence between our original domain and this rigid polynomial domain.
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