Geometric Complex Coordinates for Teichmüller Space
Geometric Complex Coordinates for Teichmüller Space
复制标题
Teichmüller 空间的几何复坐标
DOI：
10.1142/9789812798411_0016
复制
发表时间：
1987
影响因子：
4.9
通讯作者：
A. Marden
中科院分区：
文献类型：
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作者：
A. Marden
本文的目的是报告我和Clifford Earle在几年前发现的teichm<e:1>空间的复坐标系统。第一个复坐标系是由Ahlfors建立的，早期的工作是由Rauch完成的。Ahlfors坐标是局部坐标，它们是由全纯微分的变化、零点和周期给出的。最广泛使用的坐标是bers[2]的坐标，它是间接给出的，现在被称为kleinian群的准fuchsian空间的bersslices。其他用克莱因群表示的坐标是Maskit [11]；参见Kra[8]。在这里，我们将描述全局的，几何的，并且像Ahlfors一样，直接涉及黎曼曲面的坐标。事实上，它们是由一种长期使用的充气装置引起的。它们在计算曲面退化对解析表达式的影响的渐近展开式时具有特殊的价值。
The purpose of this note is to report on a system of complex coordinates for Teichmüller space that Clifford Earle and I found several years ago. The first complex coordinate system was established by Ahlfors [1], with earlier work by Rauch. Ahlfors' coordinates are local ones, and they are given in terms of the variation of a holomorphic differential, its zeros, and its periods. The most widely used coordinates are those of Bers [2] which are given indirectly in terms of what is now called Bers slices of the quasifuchsian space of kleinian groups. Other coordinates that are given in terms of kleinian groups are those of Maskit [11]; see also Kra [8].Here we will describe coordinates that are at once global, geometric, and, like Ahlfors', directly involve the Riemann surfaces. In fact they arise from a long used device for blowing up punctures. They are of special value in computing asymptotic expansions for the effect of the degeneration of a surface on the analytic expressions on the surface.