Hyperbolically Bi-Lipschitz Continuity for 1|w|2-Harmonic Quasiconformal Mappings

Abstract EN

We study the class of 1/|w|2-harmonic K-quasiconformal mappings with angular ranges.

After building a differential equation for the hyperbolic metric of an angular range, we obtain the sharp bounds of their hyperbolically partial derivatives, determined by the quasiconformal constant K.

As an application we get their hyperbolically bi-Lipschitz continuity and their sharp hyperbolically bi-Lipschitz coefficients.