论文标题
在朱莉娅（Julia）限制方向上
On Julia limiting directions in higher dimensions
论文作者
论文摘要
在本文中，我们首次研究了朱莉娅（Julia）在$ \ mathbb {r}^n $ of thromencentental-type中限制了Quasiregular映射的方向。首先，我们给出条件，每个方向都是朱莉娅限制方向。在此过程中，我们的方法表明，如果准拟合组件包含一个部门域，那么该扇区的生长就存在多项式结合。其次，我们在$ \ mathbb {r}^3 $确定哪种紧凑型子集的$ s^2 $中为反问题做出了贡献。这里的方法将需要表明$ \ mathbb {r}^3 $中的某些部门域是环境的quasiballs，这是对确定哪个域的众所周知的困难问题的贡献，是单位球$ \ m athbb {b}^3 $在$ \ mathbb $ \ mathbbbbbbbb的环境quasiconformal下的图像。
In this paper we study, for the first time, Julia limiting directions of quasiregular mappings in $\mathbb{R}^n$ of transcendental-type. First, we give conditions under which every direction is a Julia limiting direction. Along the way, our methods show that if a quasi-Fatou component contains a sectorial domain, then there is a polynomial bound on the growth in the sector. Second, we give a contribution to the inverse problem in $\mathbb{R}^3$ of determining which compact subsets of $S^2$ can give rise to Julia limiting directions. The methods here will require showing that certain sectorial domains in $\mathbb{R}^3$ are ambient quasiballs, which is a contribution to the notoriously hard problem of determining which domains are the image of the unit ball $\mathbb{B}^3$ under an ambient quasiconformal map of $\mathbb{R}^3$ to itself.
