Quasiconformal Isotopies
Quasiconformal Isotopies
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DOI：
10.1007/978-1-4613-9602-4_12
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
D. Drasin;C. Earle;F. Gehring;A. Marden
中科院分区：
文献类型：
--
作者：
D. Drasin;C. Earle;F. Gehring;A. Marden
设X是一个可能具有无限拓扑复杂性的双曲黎曼曲面或双曲黎曼曲面。设？：X→X是拟共形映射。我们证明了下列条件是等价的(§1)：(A)通过一致拟共形映射，对S_1上的恒等式--泛覆盖Δ有一个提升；(B)？同伦于X的理想边界上的恒等式；(C)通过一致拟共形映射，？与X的理想边界同伦。
LetXbe a hyperbolic Riemann surface or orbifold, possibly of infinite topological complexity. Let Ø: X → X be a quasiconformal map. We show the following conditions are equivalent (§1):(a)Ø has a lift to the universal cover Δ which is the identity on S1;(b)Ø is homotopic to the identity rel the ideal boundary of X; and(c)Ø is isotopic to the identity rel ideal boundary, through uniformly quasiconformal maps.