Prime ends in metric spaces and quasiconformal-type mappings
Prime ends in metric spaces and quasiconformal-type mappings
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素数以度量空间和拟共形类型映射结束
DOI：
10.1007/s13324-019-00292-z
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发表时间：
2019
影响因子：
1.7
通讯作者：
Tomasz Adamowicz
中科院分区：
文献类型：
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作者：
Tomasz Adamowicz
通过使用内径距离条件，我们定义和调查新的，在这样的一般性，类$${\mathcal {F}}$$F的同胚域之间的度量空间和显示，在额外的假设下，域，$${\mathcal {F}}$$F包含（拟）共形，双Lipschitz和拟对称映射的例子说明。此外，我们采用一个素数结束理论在度量空间，并提供条件，允许连续和同胚扩展的映射在$${\mathcal {F}}$$F拓扑闭包的域，以及同胚扩展的素数结束边界。满足有界转向条件的区域，在边界处局部连通和非连通的区域以及这种区域的素端边界的结构在我们的研究中起着至关重要的作用。我们应用我们的结果显示Koebe定理弧极限的映射$${\mathcal {F}}$$F。此外，罗伊登边界和素端边界之间的关系。我们的工作概括的结果由于Carathéodory，Näkki，Väisälä和Zoriodi。
By using the inner diameter distance condition we define and investigate new, in such a generality, class $${\mathcal {F}}$$F of homeomorphisms between domains in metric spaces and show that, under additional assumptions on domains, $${\mathcal {F}}$$F contains (quasi)conformal, bi-Lipschitz and quasisymmetric mappings as illustrated by examples. Moreover, we employ a prime ends theory in metric spaces and provide conditions allowing continuous and homeomorphic extensions of mappings in $${\mathcal {F}}$$F to topological closures of domains, as well as homeomorphic extensions to the prime end boundary. Domains satisfying the bounded turning condition, locally and finitely connected at the boundary and the structure of prime end boundaries for such domains play a crucial role in our investigations. We apply our results to show the Koebe theorem on arcwise limits for mappings in $${\mathcal {F}}$$F. Furthermore, relations between the Royden boundary and the prime end boundary are presented. Our work generalizes results due to Carathéodory, Näkki, Väisälä and Zorič.
不可接近素端的素端容量、分辨率和凯洛格性质
影响因子：
0.8
作者：
Adamowicz, Tomasz;Shanmugalingam, Nageswari
通讯作者：
Shanmugalingam, Nageswari