The modulus method for nonhomeomorphic quasiconformal mappings

The modulus method is one of the most effective methods in the theory of quasiconformal homeomorphisms. Over the course of a long time there has been no success, however, in applying this method to the analysis of nonhomeomorphic quasiconformal mappings of spatial domains.
In the present paper inequalities are established for the moduli of families of curves corresponding with each other under a certain, not necessarily homeomorphic, quasiconformal mapping. These inequalities are applied to the study of the relation of dilatation with the minimal multiplicity of a ramification of such mappings.
Bibliography: 7 titles.