Anatoly Golberg
Holon Institute of Technology, Holon, Israel

Our main goal in the present talk is to extend the Teichmüller theorem on separating rings to higher dimensions (a main problem here is that there is no analogue of the Uniformization Theorem in $\mathbb R^n,$ $n\ge 3$). In addition, we apply this result to studying the boundary correspondence problems. We emphasize that our approach may allow us to weaken regularity for quasiconformality assumptions of the mappings. Such applications to mappings of finite directional dilatations will be also presented. The talk is based on joint works with T. Sugawa and M. Vuorinen.