Abstract:
We continue the study of the problem on unique determination of domains in Euclidean spaces by the relative conformal moduli of their boundary condensers. The main result asserts that every convex bounded polyhedral domain in the three-dimensional Euclidean space is uniquely determined by the relative conformal moduli of its boundary condensers. An analogous result was earlier obtained for $n$-dimensional polyhedral domains in the case $n \ge 4$.
Keywords:$p$-modulus of a path family, boundary condenser, conformal mapping, isometry, unique determination.