Abstract
The inverse of a K-quasiconformal homeomorphism is also K-quasiconformal. By the Schwarz lemma for K-quasiconformal mappings we know that both mappings are Hölder continuous in the Euclidean metric with exponent K 1∕(1−n), and the Gehring–Osgood result yields the same conclusion in the quasihyperbolic metric. The class of harmonic K-quasiconformal interpolates between the classes of conformal maps and general quasiconformal maps. In this chapter we study the modulus of continuity of harmonic quasiconformal mappings relative to the quasihyperbolic metric and prove that both the mapping and its inverse are Lipschitz-continuous.
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Todorčević, V. (2019). Bi-Lipschitz Property of HQC Mappings. In: Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics. Springer, Cham. https://doi.org/10.1007/978-3-030-22591-9_5
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DOI: https://doi.org/10.1007/978-3-030-22591-9_5
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