Hyperbolically Bi-Lipschitz Continuity for1/|w|2-Harmonic Quasiconformal Mappings

摘要

We study the class of1/|w|2-harmonicK-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 constantK. As an application we get their hyperbolically bi-Lipschitz continuity and their sharp hyperbolically bi-Lipschitz coefficients.