Ukrainian Mathematical Bulletin

Volume 1, Issue 2, 2004 pp. 153-176.

Estimates of Rotation under Conformal and Quasiconformal Mappings

Authors: V.Ya.Gutlyanskii and O.Martio
Author institution: Institute of Applied Mathematics and Mechanics, of the Ukrainian National Academy of Sciences, Department of Mathematics, University of Helsinki, Finland

Summary: The extremal problem of sharp estimates of an arbitrary functional depending on the argument of the derivative and angular displacements at a fixed point is solved in a class S of univalent analytic functions defined in a unit disk. The solution is based on the Lowner differential equation and the reduction of the problem to the well-known Caratheodory class. New John--Belinskii-type estimates are established for the rotation of radial segments under quasiconformal mappings in the plane.

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