Quasi-isometricity and Equivalent Moduli of Continuity of Planar 1/|\omega|^2-Harmonic Mappings

Qi Yi, Shi Qingtian


In this paper, we prove that 1/|\omega|^2-harmonic quasiconformal mapping is bi-Lipschitz continuous with respect to quasihyperbolic metric on every proper domain of C\{0}. Hence, it is hyperbolic quasiisometry
in every simply connected domain on C\{0}, which generalized the result obtained in [14]. Meanwhile, the equivalent moduli of continuity for 1/|\omega|^2-harmonic quasiregular mapping are discussed as a by-product.

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