Filomat 2015 Volume 29, Issue 2, Pages: 335-341
https://doi.org/10.2298/FIL1502335K
Full text ( 244 KB)
A note on the harmonic quasiconformal diffeomorphisms of the unit disc
Knežević Miljan (Faculty of Mathematics, Belgrade)
We analyze the properties of harmonic quasiconformal mappings and by
comparing some suitably chosen conformal metrics defined in the unit disc we
obtain some geometrically motivated inequalities for those mappings (see for
instance [15, 17, 20]). In particular, we obtain the answers to many
questions concerning these classes of functions which 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 is geometrical in nature, via
analyzing the properties of the Gaussian curvature of the conformal metrics
we are dealing with. As a consequence of this approach we give a note to the
co-Lipschicity of harmonic quasiconformal self mappings of the unit disc at
the origin.
Keywords: harmonic mappings, quasiconformal mappings, hyperbolic metrics, Quasi-isometry
Projekat Ministarstva nauke Republike Srbije, br. ON174032