Quasiconformal mappings on the Heisenberg group: An overview

Abstract

We present a brief overview of the Korányi-Reimann theory of quasiconformal mappings on the Heisenberg group stressing on the analogies as well as on the differences between the Heisenberg group case and the classical two-dimensional case. We examine the extensions of the theory to more general spaces and we state some known results and open problems.

arXiv comment15 pages, some typos and misplacements from the previous version have been corrected. This article will appear in the Handbook of Teichmüller Theory, vol. VI (Athanase Papadopoulos, ed.)