Proper holomorphic mappings between symmetrized ellipsoids

Abstract

Abstract.We characterize the existence of proper holomorphic mappings in the special class of bounded (1, 2, . . . , n)-balanced domains in C n , called the symmetrized ellipsoids. Using this result we conclude that there are no non-trivial proper holomorphic self-mappings in the class of symmetrized ellipsoids. We also describe the automorphism groups of these domains. Mathematics Subject Classification (2010). 32H35, 32A07.