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Abstract:
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This thesis considers various properties of Euclidean harmonic mappings, quasiconformal
mappings and generalized harmonic mappings, which are harmonic with
respect to the conformal metric on the image surface. In particular, we obtained the
answers to many questions concerning these classes of functions and that are related
to the determination of different properties that are of essential importance for validity
of the results such as those that generalize famous inequalities of the Schwarz-Pick
type. The approach used was geometrical in nature, via analyzing the properties of
the Gaussian curvature of the conformal metrics we are dealing with. |