We study the hyperbolically Lipschitz continuity, Euclidean and hyperbolic area distortion theorem, and coefficient estimates for the classes of (K, K′)-quasiconformal harmonic mappings from the unit disk onto itself.
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A. Hernándezmontes and L. O. Reséndis, “Area distortion under certain classes of quasiconformal mappings,” J. Inequal. Appl., 2017, Article 211 (2017).
D. Kalaj and M. Mateljević, “(K, K′)-quasiconformal harmonic mappings,” Potential Anal., 36, 117–135 (2012).
D. Kalaj, “On quasiconformal harmonic maps between surfaces,” Int. Math. Res. Not. IMRN, 2, 355–380 (2015).
D. Kalaj, “On harmonic quasiconformal self-mappings of the unit ball,” Ann. Acad. Sci. Fenn. Math., 33, 261–271 (2008).
D. Partyka and K. Sakan, “On bi-Lipschitz type inequalities for quasiconformal harmonic mappings,” Ann. Acad. Sci. Fenn. Math., 32, 579–594 (2007).
E. Heinz, “On one-to-one harmonic mappings,” Pacific J. Math., 9, 101–105 (1959).
J. Zhu, “Coefficients estimate for harmonic v-bloch mappings and harmonic K-quasiconformal mappings,” Bull. Malays. Math. Sci. Soc., 39, No. 1, 349–358 (2016).
K. Astala, “Area distortion of quasiconformal mappings,” Acta Math., 173, 37–60 (1994).
M. Chen and X. Chen, “(K, K′)-quasiconformal harmonic mappings of the upper half plane onto itself,” Ann. Acad. Sci. Fenn. Math., 37, 265–276 (2012).
M. Knězević and M. Mateljević, “On the quasi-isometries of harmonic quasiconformal mappings,” J. Math. Anal. Appl., 334, 404–413 (2007).
M. Pavlović, “Boundary correspondence under harmonic quasiconformal homeomorphisms of the unit disk,” Ann. Acad. Sci. Fenn. Math., 27, 365–372 (2002).
O. Martio, “On harmonic quasiconformal mappings,” Ann. Acad. Sci. Fenn. Math., 425, 3–10 (1968).
R. M. Porter and L. F. Reséndis, “Quasiconformally explodable sets,” Complex Var. Theory Appl., 36, 379–392(1998).
T. Wan, “Constant mean curvature surface, harmonic maps, and universal Teichm¨uller space,” J. Different. Geom., 35, 643–657 (1992).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 2, pp. 151–159, February, 2021. Ukrainian DOI: 10.37863/umzh.v73i2.6041.
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Zhong, D., Yuan, W. Hyperbolically Lipschitz Continuity, Area Distortion, and Coefficient Estimates for (K, K′)-Quasiconformal Harmonic Mappings of the Unit Disk. Ukr Math J 73, 171–180 (2021). https://doi.org/10.1007/s11253-021-01916-z
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DOI: https://doi.org/10.1007/s11253-021-01916-z