SIMULTANEOUS UNIFORMIZATION
SIMULTANEOUS UNIFORMIZATION
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同步统一化
DOI：
10.1090/s0002-9904-1960-10413-2
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发表时间：
1963
期刊：
影响因子：
3.7
通讯作者：
L. Bers
中科院分区：
文献类型：
--
作者：
L. Bers
证明了满足一定条件的任意两个黎曼曲面，如同一亏格g>；L的任意两个闭曲面，都可以由一组分式线性变换(定理1)统一。这与以前的结果[2；3]相结合，导致给定亏格的所有代数曲线的同时均匀化(定理2-4)。定理5包含对无限维Teichmtiller空间的一个应用。设S是抽象黎曼曲面，ƒ是S的有界偏心率到S的有界离心率到另一个抽象黎曼曲面上的同态，[f]是/的同伦类。我们称(S，[ƒ]，S‘)为一对偶合黎曼曲面，一偶(奇)偶若/保(反)向。两个耦合对(S，[ƒ]，S‘)和(Si，[FI]，S’)称为等价的，如果存在一致同胚h和hr，且h(S)=Si，h‘(S)
We shall show that any two Riemann surfaces satisfying a certain condition, for instance, any two closed surfaces of the same genus g> l, can be uniformized by one group of fractional linear transformations (Theorem 1). This leads, in conjunction with previous results [2; 3], to the simultaneous uniformization of all algebraic curves of a given genus (Theorems 2-4). Theorem 5 contains an application to infinitely dimensional Teichmtiller spaces.1. Let S be an abstract Riemann surface, ƒ a homeomorphism of bounded eccentricity of S onto another such surface S', and [f] the homotopy class of/. We call (S,[ƒ], S') a coupled pair of Riemann surfaces, an even (odd) pair if/preserves (reverses) orientation. Two coupled pairs,(S,[ƒ], S') and (Si,[fi], S') are called equivalent if there exist conformai homeomorphisms h and hr with h (S)= Si, h'(S)