论文标题

剪切地图和单位球的跑步地图,该图不会嵌入具有$ \ mathbb c^n $的Loewner链中

Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range $\mathbb C^n$

论文作者

Bracci, Filippo, Gumenyuk, Pavel

论文摘要

在本文中,我们研究了$(z,w)\ mapsto(z+g(w),w)$的单位球的“剪切”式图像的类别。除了一般属性外,我们还使用此类地图来构建一个标准化的球映射的示例,以$ \ Mathbb c^n $中的runge域上构建,但是该范围无法嵌入到Loewner链中,其范围为$ \ Mathbb c^n $。

In this paper we study the class of "shearing" holomorphic maps of the unit ball of the form $(z,w)\mapsto (z+g(w), w)$. Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in $\mathbb C^n$ which however cannot be embedded into a Loewner chain whose range is $\mathbb C^n$.

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