Abstract
Historically the origin of quasiconformal mappings is connected with developments of the methods of complex functions. Since the power of this concept was first realized, quasiconformal mappings have engaged the attention of many prominent mathematicians and the theory has been greatly expanded to higher dimensions. The fundamental principle of this theory is to interpolate between diffeomorphisms and homeomorphisms [G4]. One difference between conformal and quasiconformal mappings is that the latter need not be differentiable in the usual sense. However, by a theorem due to A. Mori, F. W. Gehring and J. Viiisiilii, every quasiconformal mapping f : n --t Rn is differentiable almost everywhere and its Jacobian determinant .J(x, f) is locally integrable. Moreover, quasiconformality of f can be expressed by the differential inequality
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