NC\({}_ p\)-sets of finite area (Q803321)

In the paper, the author shows that the set \(B_ f\) of all branching points of a mapping f:G \(\to {\mathbb{R}}^ n\) with a bounded distortion, having a finite (n-1)-dimensional Hausdorff measure, is the so-called \(NC_ p\)-set [\textit{W. M. Gol'dshtein} and \textit{Yu. G. Reshetnyak}, An introduction to the theory of functions with generalized derivatives and quasiconformal mappings, Moscow; Science 1983] in the region G for each \(p\in (1,+\infty)\). He also shows that, for such mappings, the full pre- images of an \(NC_ n\)-set is an \(NC_ n\)-set and finds a structure formula for an \(NC_ p\)-set of a finite (n-1)-dimensional Hausdorff measure.