Authors: Guowu Yao
Publish Date: 2007/03/13
Volume: 122, Issue: 4, Pages: 375-389
Abstract
In this paper the asymptotic boundary behavior of a Hopf differential or the Beltrami coefficient of a harmonic map is investigated and certain compact properties of harmonic maps are established It is shown that if f is a quasiconformal harmonic diffeomorphism between two Riemann surfaces and is homotopic to an asymptotically conformal map modulo boundary then f is asymptotically conformal itself In addition we prove that the harmonic embedding map from the Bers space B Q D X of an arbitrary hyperbolic Riemann surface X to the Teichmüller space T X induces an embedding map from the asymptotic Bers space A B Q D X a quotient space of B Q D X into the asymptotic Teichmüller space AT X
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