Quasihyperbolic metric and Quasisymmetric mappings in metric spaces
Quasihyperbolic metric and Quasisymmetric mappings in metric spaces
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DOI：
10.1090/s0002-9947-2015-06240-0
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发表时间：
2015-02
影响因子：
1.3
通讯作者：
Xiaojun Huang;Jinsong Liu
中科院分区：
文献类型：
--
作者：
Xiaojun Huang;Jinsong Liu
本文证明了拟双曲度量在两个适当的度量空间之间的拟对称映射下是拟不变的。同时，我们还证明了拟双曲度量的拟不变性意味着相应的映射是拟共形的。最后，作为上述定理的应用，我们证明了度量空间中两个拟对称映射的复合是拟共形映射。
In this paper, we prove that the quasihyperbolic metrics are quasiinvariant under a quasisymmetric mapping between two suitable metric spaces. Meanwhile, we also show that quasi-invariance of the quasihyperbolic metrics implies that the corresponding map is quasiconformal. At the end of this paper, as an application of above theorems, we prove that the composition of two quasisymmetric mappings in metric spaces is a quasiconformal mapping.