调和映照的双Lipschitz性质
Bi-Lipschitz Properties for Harmonic Mappings

设$w(z)$为单位圆盘$\mathbf{U}$到约当区域$\Omega\subseteq \mathbf{C}$上的 调和映照. 给出$w(z)$具有Lipschitz性质的等价条件. 进一步地, 若$\Omega$为有界凸区域, 对其边界函数给出一个较弱的条件, 使得$w=P[f](z)$为调和拟共形映照.
Suppose that $w(z)$ is a harmonic mapping of the unit disk $\mathbf{U}$ onto a Jordan domain $\Omega\subseteq \mathbf{C}$. The author finds some equivalent conditions for the Lipschitz property of $w(z)$. Moreover, if $\Omega$ is a bounded convex domain, a weaker condition on the boundary function $f$ is found, such that $w(z)=P[f](z)$ is a harmonic quasiconformal mapping.