On Belinskii conformality in countable sets of points

Vladimir I. Ryazanov, Matti K. Vuorinen
2001 Proceedings of the American Mathematical Society  
The local behavior of plane quasiconformal mappings is investigated. In particular, generalizing the well-known Reich-Walczak problem, we study the possibility for a quasiconformal mapping to be conformal in the sense of Belinskii at a prescribed point or in a prescribed set of points when the modulus of the complex dilatation is a fixed measurable function. The notion of the Belinskii conformality is related to the conception of asymptotical rotations by Brakalova and Jenkins.
doi:10.1090/s0002-9939-01-05932-9 fatcat:jywa3p6hirev3k4xhea6tj2gfy