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《科学通报(英文版)》 1997-24
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On the boundary value problem for harmonic maps of the Poincaré disc

LI ZhongDepartment of Mathematics, Peking University, Beijing 100871, China  
The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfyingwhere ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with normsIt is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B .
【CateGory Index】: O157.5
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Chinese Journal Full-text Database 10 Hits
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8 Wang Chaoxiang Huang Xinzhong Department of Mathematics, Huaqiao University, 362021, Quanzhou, China;On the Extension Theorem for Zygmund Functions in Closed Interval[J];Journal of Huaqiao University(Natural Science);2006-02
9 ZHU Jian-feng,HUANG Xin-zhong(Department of Mathematics,Huaqiao University,Quanzhou 362021,China);The Extension Theorem of Quasisymmetric Function on the Interval[J];Journal of Huaqiao University(Natural Science);2007-01
10 LIN Zhen-lian(School of Mathematics Science,Huaqiao University,Quanzhou 362021,China);A Note on the Paper of the Generalization of Beurling-Ahlfors′ Extension[J];Journal of Huaqiao University(Natural Science);2007-03
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