根据共形度量定义的Schwarz导数和Ahlfors关于曲线的Schwarz导数的定义,结合新的共形因子λ(z)=√|h'(z)|^2+|g'(z)|^2)来讨论调和映射f的Weierstrass-Enneper提升f~的单叶性条件和f~在单位圆内的两点偏差定理的定量形式。
In this paper we obtain a general criterion in terms of the Schwarzian derivative for global univalence of the Weierstrass-Enneper lift of a planar harmonic mapping and turn out that the harmonic lift f~ satisfies a two-point distortion condition. The analysis depends on a generalized Schwarzian defined for eonformal metrics and on a Schwarzian introduced by Ahlfors for curves.