Lipschitz conditions, triangular ratio metric, and quasiconformal maps

By Jiaolong Chen, Parisa Hariri, R. Kl'en, Matti Vuorinen. 2014

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ea88b78e91564daaf92cdaf9ec0066d8d90b71be