Lipschitz conditions, triangular ratio metric, and quasiconformal maps
: Jiaolong Chen, Parisa Hariri, Riku Klén, Matti Vuorinen
: 2015
: Annales Academiae Scientiarum Fennicae. Mathematica
: aasfm
: 40
: 2
: 683
: 709
: 27
: 1239-629X
DOI: https://doi.org/10.5186/aasfm.2015.4039
: http://www.acadsci.fi/mathematica/Vol40/vol40.html
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.