Geometry of Metrics
  During the past thirty years hyperbolic type metrics have become popular tools also in modern mapping theory, e.g., in the study of quasiconformal and quasiregular maps in the euclidean $n$-space. We study here several metrics that one way or another are related to modern mapping theory and point out many open problems dealing with the geometry of such metrics. 
Matti Vuorinen
math.CV