Lipschitz conditions, triangular ratio metric, and quasiconformal maps

Lipschitz conditions, triangular ratio metric, and quasiconformal maps
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DOI：
10.5186/aasfm.2015.4039
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发表时间：
2014-03
期刊：
arXiv: Classical Analysis and ODEs
影响因子：
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通讯作者：
Jiaolong Chen;Parisa Hariri;R. Kl'en;M. Vuorinen
Jiaolong Chen;Parisa Hariri;R. Kl'en;M. Vuorinen
中科院分区：
其他
文献类型：
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作者：
Jiaolong Chen;Parisa Hariri;R. Kl'en;M. Vuorinen

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研究了复平面和欧氏空间子域上的三角比度量.证明了它的各种不等式，主要结果讨论了这种度量在拟共形映射下的行为。我们还研究了小半径度量圆盘的光滑性。
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the smoothness of metric disks with small radii.