标题： 格林映射和朱利亚集 显示英文标题

标题： Greenś Mapping and Julia Sets

摘要： 1999年3月，第一作者（Binder）提出了一个问题是证明对于任何Green映射$T:H\rightarrow\tilde \Omega$存在一个“良好方向”$\psi\in [0,2]$，即\begin{equation}\label{binder} \int\limits_0\limits^{1} |T''(re^{i\pi\psi})|dr <\infty, \quad\text{ for at least one } \quad \psi\in [0,2]. \end{equation}目前即使在$\partial \Omega $是实直线上的一个均匀完美子集的特殊情况下，这个问题仍然未解决。 在本文中，当$\Omega = \overline{C} \setminus E_0$时我们得到了一个正解，其中$E_0 \subset R $是一个扩张二次多项式的Julia集。 显示英文摘要

摘要： In March 1999, the first named author (Binder) posed the problem of showing that a ``good direction'' $\psi\in [0,2]$ exists, for any Green's mapping $T:H\rightarrow\tilde \Omega$, i.e., \begin{equation}\label{binder} \int\limits_0\limits^{1} |T''(re^{i\pi\psi})|dr <\infty, \quad\text{ for at least one } \quad \psi\in [0,2]. \end{equation} Presently this problem is open even in the special case where $\partial \Omega $ is a uniformly perfect subset of the real line. In this paper we obtain a positive solution when $\Omega = \overline{C} \setminus E_0$ where $E_0 \subset R $ is the Julia set of an expanding quadratic polynomial.