Abstract
We are analyzing the properties of holomorphic functions and the hyperbolic metric to obtain some geometrically motivated inequalities for quasi-conformal and generalized harmonic mappings. Also, we are interested in which properties of hyperbolic harmonic mappings and the hyperbolic metric are essential for validity of some versions of the Ahlfors–Schwarz lemma.
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References
Gardiner, F.P.: Teichmüller Theory and Quadratic Differentials. Awiley-Interscience Publication, New York (1987)
Kalaj, D.: Univalent Harmonic Mappings Between Jordan Domains, vol. 69, br. 83, str. 108–112. Publications de l’Institut Mathematique (2001)
Kraus, D., Roth, O., Ruscheweyh, S.: A boundary version of Ahlfors Lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps. J. d’Analyse Math. 101(1), 219–256 (2007)
Knežević, M., Mateljević, M.: On the quasi-isometries of harmonic quasiconformal mappings. Journal of Mathematical Analysis and Applications, 334(1), 404–413 (2007)
Mateljevic, M.: Dirichlet’s principle, distortion and related problems for harmonic mappings, Publication l’Inst Math -Belgrade, nouvelle serie 75(89), 147–171 (2004) (special number Quasiconformal and Harmonic mappings, special guest editor M. Mateljević), ISSN 0350–1302
Mateljević, M., Božin, V., Knežević, M.: Quasiconformality of harmonic mappings between Jordan domains. FILOMAT 24(3), 111–122 (2010)
Schoen, R., Yau, S.T.: Lectures on Harmonic Maps, Conf. Proc. and Lect. Not. in Geometry and Topology, vol. II. International Press, Cambridge (1997)
Wan, T.: Conastant mean curvature surface, harmonic maps, and univrsal Teichmüller space. J. Diff. Geom. 35, 643–657 (1992)
Acknowledgements
This note was supported by the project ON174032 of the Serbian Ministry of Education, headed by professor M. Mateljević. In addition, I would also like to thank professor V. Dobrev and professor B. Dragovich since I had the opportunity to take a part at the LT conferences in Varna.
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Knežević, M. (2013). Some Properties of Harmonic Quasi-Conformal Mappings. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_40
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DOI: https://doi.org/10.1007/978-4-431-54270-4_40
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