On Belinskii conformality in countable sets of points

Ryazanov, Vladimir; Vuorinen, Matti

doi:10.1090/S0002-9939-01-05932-9

On Belinskii conformality in countable sets of points
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by Vladimir I. Ryazanov and Matti K. Vuorinen PDF

Proc. Amer. Math. Soc. 129 (2001), 3049-3056 Request permission

Abstract:

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.

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