Characterization of ring \(Q\)-homeomorphisms on Riemann manifolds (Q2901754)

The so-called ring \(Q\)-homeomorphisms introduced recently are studied in the present paper. More precisely, the work is devoted to the study of some analogues of quasiconformal mappings on manifolds in which the notion of the modulus of a family of paths can be given. For such manifolds, the author gives the definition of a ring \(Q\)-homeomorphisms at a point in the spirit of the geometric definition of quasiconformality by J. Väisälä. The main result of the article states the connection of the above definition with the verification of the condition of special type. The result is an extension of the corresponding theorem proved earlier for \({\mathbb R}^n\).