Abstract
In this note we determine the automorphism group of complex manifolds which are proper images of a simply connected strictly pseudoconvex domain in ℂn. We also investigate automorphisms of domains invariant under a compact subgroup of complex linear transformations. Furthermore, some regularity and rigidity properties of proper holomorphic mappings are established. In particular we solve a question raised by Hahn and Pflug regarding the nonexistence of proper holomorphic mappings between the euclidian ball and the complex minimal ball of ℂn.
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