Lipschitz conditions, triangular ratio metric, and quasiconformal maps
  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. 
Jiaolong Chen, Parisa Hariri, Riku Kl\'en, Matti Vuorinen
math.CA