Polydisc

In the multi-dimensional function theory of polycylinder is the Cartesian product of circular disks.

Is referred to in more detail with an open disk in the complex plane, then the polycylinder is added to the point with the multi- radius than

Or equivalently as

Polycylinder the ball is the same as the Euclidean a generalization of the one-dimensional circular disk. For these two quantities are not biholomorphic equivalent. This statement was proved by Poincaré in 1907, by showing that the automorphism groups of the two quantities as Lie groups have different dimension.