Holomorphic embeddings and applications

Abstract: In the first part of this thesis we consider the question of the number of equivalenceclasses of holomorphic embeddings of Ck into Cn. We show the existence of holomorphicfamilies of proper holomorphic embeddings of Ck into Cn (0 < k < n?1),such that members of the family are pairwise nonequivalent in a suitable sense. Asan application we use these embeddings to deduce results in the theory of holomorphictransformation groups.In the second part of the thesis the question of plurisubharmonic extension is connectedto analytic discs, i.e. nonconstant holomorphic maps of the unit disc in Cinto Cn. We derive results on plurisubharmonic extension for analytic polyhedra.