Boundary Behavior

Many results of the boundary behavior of the theory of planar analytic functions have their counterparts for qr mappings for all dimensions n ≥ 2. In the early stage of the development of the theory some of these counterparts were established by O. Martio and S. Rickman [MR1]. Later M. Vuorinen continued this line of research in a number of articles, see 2.3 and 7.4. The tool in [MR1] and mostly in Vuorinen’s articles is the method of extremal length. S. Granlund, P. Lindqvist, and O. Martio introduced for a given variational kernel F in [GLM2] a substitute for the harmonic measure, called F-harmonic measure. This potential theoretic notion has turned out to be a useful tool when studying the properties of qr mappings near the boundary.