Automorphisms and equivalence of bounded Reinhardt domains not containing the origin (Q1103753)

The author gives an answer to the equivalence problem for bounded Reinhardt domains, that is, domains in \({\mathbb{C}}^ n\) which are invariant under rotation about the coordinate axes. This problem has already been solved for Reinhardt domains containing the origin, see \textit{T. Sunada}, Math. Ann. 235, 111-128 (1978; Zbl 0357.32001), and for Reinhardt domains containing some points with ith coordinate zero for \(0\leq i\leq k\) and no points with ith coordinate zero for \(k+1\leq i\leq n\) for some k, see \textit{D. Barrett}, Comment. Math. Helv. 59, 550-564 (1984; Zbl 0601.32030). The author also determines the automorphisms of a certain class of bounded Reinhardt domains not containing the origin. His approach is primarily group-theoretic as opposed to the analytic techniques of Barrett and Bedford [\textit{E. Bedford}, Pac. J. Math. 87, 271-281 (1980; Zbl 0449.32024)].