Weakly pseudoconvex domains with non-compact automorphism groups
The main theorem of this paper is that if \(F_ i: \Omega _ 1\to \Omega _ 2\) is a sequence of biholomorphic mappings between weakly pseudoconvex domains in \({\mathbb{C}}^ n\) with real analytic boundaries such that \(F_ i\) converges uniformly on compact subsets of \(\Omega _ 1\) to a mapping F, then there is a domain D which contains \(\Omega _ 1\) together with all the strictly pseudoconvex boundary points of \(\Omega _ 1\) with the following property: the mappings \(F_ i\) and the mapping F extend holomorphically to D. Furthermore, \(F_ i\) converges uniformly on compact subsets of D to F. The mapping F is either a constant map of \(\Omega _ 1\) into the set of weakly pseudoconvex boundary points of \(\Omega _ 2\), or F is a biholomorphic map. This theorem is a first step toward proving that the class of weakly pseudoconvex domains with non- compact automorphism groups must be small.
biholomorphic mappings between weakly pseudoconvex domains
scientific article; zbMATH DE number 4000371