Abstract

It was proved by the authors that given a quasiconformal harmonic diffeomorphism F on H², there is a neighborhood N of the class F represented by F in the universal Teichmüller space such that if H in N, then the boundary map of H can be extended to a quasiconformal harmonic diffeomorphism on H², i.e. the class H can be represented by a quasiconformal harmonic diffeomorphism. More precisely, it was proved that if F is a quasiconformal harmonic diffeomorphism on H², and if G is a quasiconformal map on H² such that the dilatation of G is small enough, then there exists quasiconformal harmonic diffeormophisms with the same boundary data with F ∘ G and G ∘ F. The purposes of this paper is to study the higher dimensional generalization to this result and related problems.

Authors