Asymptotic Teichmuller space of a closed set of the Riemann sphere
Asymptotic Teichmuller space of a closed set of the Riemann sphere
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黎曼球面闭集的渐近 Teichmuller 空间
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通讯作者：
Wu Yan
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作者：
Qi Yi;Wu Yan
引入了Riemann球面C的闭子集E的至少4点的渐近Teichmuller空间AT(E)和自然渐近Teichmuller度量.证明了AT(E)等距同构于连通分支的渐近TeichMuller空间与E上的Beltrami Coefficients defi的Banach空间的乘积空间，并证明了AT(E)上存在复Banach流形结构.
The asymptotic Teichmuller space AT(E) of a closed subset E of the Riemann sphere C with at least 4 points and the natural asymptotic Teichmuller metric are introduced. It is proved that AT(E) is isometrically isomorphic to the product space of asymptotic Teichmuller spaces of the connected components of C \ E and the Banach space of Beltrami coefficients defined on E. Furthermore, it is proved that there is a complex Banach manifold structure on AT(E)..