BI-LIPSCHITZ PROPERTY AND DISTORTION THEOREMSFOR PLANAR HARMONIC MAPPINGS WITH M-LINEARLYCONNECTED HOLOMORPHIC PART

摘要

Let f=h+g be a harmonic mapping of the unit disk Dwith the holomorphic part h satisfying that h is injective and h(D) isan M-linearly connected domain. In this paper,we obtain the sufficientand necessary conditions for f to be bi-Lipschitz,which is in particular,quasiconformal. Moreover,some distortion theorems are also obtained.