Distinguished boundary of a polydisc

Summary

The distinguished boundary of a polydisc $P(a, r)$ in $\C^n$ is the torus of points with $\abs{z_j - a_j} = r_j$ for every $j$. It is the set over which the Cauchy integral formula on a polydisc integrates. A function holomorphic on the polydisc and continuous on its closure attains its largest modulus on this torus. It is the Shilov boundary of the algebra of such functions, and for $n \ge 2$ it is a small part of the topological boundary.