Prime ends in the Heisenberg group H_1 and the boundary behavior of quasiconformal mappings
Prime ends in the Heisenberg group H_1 and the boundary behavior of quasiconformal mappings
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质数以海森堡群 H_1 结尾以及拟共形映射的边界行为
DOI：
10.5186/aasfm.2018.4342
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
B. Warhurst
中科院分区：
文献类型：
--
作者：
Tomasz Adamowicz;B. Warhurst
研究了欧氏空间中扩展N-akki环的Heisenberg群的素端.相应的域类是由一致整环和Loewner性质定义的.利用素端给出了Caratheodory拟共形映射的扩张定理、弧形极限的Koebe定理、主点的Lindel定理和Tsuji定理的相应结果.
We investigate prime ends in the Heisenberg group $\mathbb{H}_{1}$ extending N\"akki's construction for collared domains in Euclidean spaces. The corresponding class of domains is defined via uniform domains and the Loewner property. Using prime ends we show the counterpart of Caratheodory's extension theorem for quasiconformal mappings, the Koebe theorem on arcwise limits, the Lindel\"of theorem for principal points and the Tsuji theorem.