Analytical foundations of the theory of quasiconformal mappings in R^n

This paper gives an exposition of basic analytical properties of quasiconformal (and quasiregular) mappings of n-dimensional domains.It grew out as a byproduct and a proper part of our work on the monograph [10] on analytic methods in the quasiconformal theory. This comes out of a general programme of studying the problems of r-dimensional quasiconformal mappings exposing and exploiting as much as possible the interconnections between the quasiconformal mappings and various problems of partial differential equations, differential geometry and classical analysis. This programme outlined in [6], [7], and essentially extende d in our plenary lecture [8] at the Conference on "Global Analysis and Differential Geometry" in Garwitz, DDR, October 1981, was based on the opinion that the natural interrelations between the quasiconformal theory in n>3 dimensions and partial dif- ferential equations, in contrast to the case n:2, have not been sufficiently explored.