The visual angle metric and quasiregular maps
The visual angle metric and quasiregular maps
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DOI：
10.1090/proc/13188
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发表时间：
2015-05
期刊：
影响因子：
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通讯作者：
Gendi Wang;M. Vuorinen
中科院分区：
文献类型：
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作者：
Gendi Wang;M. Vuorinen
研究了映射下点间距离的畸变问题。首先证明了单位圆盘上拟正则映射的一个涉及视角度量的Schwarz型引理。然后，我们反过来研究了凸域上bilipschitz映射关于视角度量的拟共形性。对于单位球或半空间，证明了关于视角度量的bilipschitz映射也是关于双曲度量的bilipschitz映射。我们还得到了各种不等式的视角度量的其他度量，如距离比度量和准双曲度量。
The distortion of distances between points under maps is studied. We rst prove a Schwarz-type lemma for quasiregular maps of the unit disk involving the visual angle metric. Then we investigate conversely the quasiconformality of a bilipschitz map with respect to the visual angle metric on convex domains. For the unit ball or half space, we prove that a bilipschitz map with respect to the visual angle metric is also bilipschitz with respect to the hyperbolic metric. We also obtain various inequalities relating the visual angle metric to other metrics such as the distance ratio metric and the quasihyperbolic metric.