Extension of correspondences between rigid polynomial domains (Q816467)

The author studies the holomorphic extension of proper holomorphic correspondences between so called rigid polynomial domains, either in \(\mathbb{C}^{2}\), or, when the domains are also convex, in \(\mathbb{C}^{n}\). The set of holomorphic extendability of such a correspondence is shown to be a dense subset of the boundary. Moreover, it is the complement of the set of boundary points \(P\) where \(\overline{\lim}_{z \rightarrow P}| f(z)| = \infty\) (\(f\) is the correspondence). It is noteworthy that pseudoconvexity of the domains is not required. In a second theorem, the author shows that if the target domain is (in addition) stronly pseudoconvex, then any irreducible correspondence is a mapping.