Reinhardt domain

Summary

A Reinhardt domain is a domain in $\C^n$ that is unchanged when each coordinate is rotated by its own angle. Such a domain is determined by the set of absolute values $(\abs{z_1}, \dots, \abs{z_n})$ of its points. Polydiscs and the unit ball are Reinhardt domains. They are the natural domains of convergence of power series in several variables. They also give the first examples of the extension phenomena of several complex variables.