Uniform continuity of quasiconformal mappings and conformal deformations
Uniform continuity of quasiconformal mappings and conformal deformations
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DOI：
10.1090/s1088-4173-08-00174-4
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发表时间：
2008-01
期刊：
影响因子：
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通讯作者：
P. Koskela;Tomi Nieminen
中科院分区：
文献类型：
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作者：
P. Koskela;Tomi Nieminen
我们证明，即使两个域都配备了内部度量，在拟双曲度量上满足适当增长条件的域上的拟共形映射也是一致连续的。与之前结果相比的改进是内部度量也可以在图像域中使用。我们还将这个结果扩展到 R 单位球上的欧几里得度量的共形变形。
We prove that quasiconformal maps onto domains satisfying a suitable growth condition on the quasihyperbolic metric are uniformly continuous even when both domains are equipped with internal metric. The improvement over previous results is that the internal metric can be used also in the image domain. We also extend this result for conformal deformations of the euclidean metric on the unit ball of R.