Unique determination of conformal type for domains. III

The article is the third (final) part of a review series entitled “Unique determination of conformal type for domains,” initiated by the author's eponymous paper, published in Sib. Èlektron. Mat. Izv., 16, 692–708 (2019). The main result of the present article is that for $n \le 3$, any $n$-connected plane domain $U$ is uniquely determined by the relative conformal moduli of pairs of boundary components.