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Non-convexity of Spheres in Infinite Dimensional Teichmiiller Spaces
Non-convexity of Spheres in Infinite Dimensional Teichmiiller Spaces

李忠
Li Zhong

Department of Mathematics, Peking University, 100871, Beijing
(Department of Mathematics, Peking University, 100871, Beijing) Communicated by Cheng Mind

收稿日期: 1993-06-25
出版日期: 1993-06-25

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摘要  Let Г be a Fuchsian group acting on the upper half plane H. We denote byBel(Г) the set of all Beltrami differentials of Г on H with L~∞-norms less than 1.For each μ∈Bel(Г) there exists a uniquely determiued quasiconformal mapping f_μ:H→H with the complex dilatation μ, which keeps 0,1 and ∞ fixed. Two elementsμ_1 and μ_2 of Bel(Г) are said to be equivalent each other if f_(μ1)|R coincides withf_(μ2) |R. Then the Teichmuller space of Г is defined to be the set of all equivalenceclasses of elements in Bel(Г).
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