On Teichmüller’s theorem on the quasi-invariance of cross ratios
On Teichmüller’s theorem on the quasi-invariance of cross ratios
复制标题
关于交叉比准不变性的Teichmüller定理
DOI：
10.1007/bf02760836
复制
发表时间：
1978
影响因子：
1
通讯作者：
I. Kra
中科院分区：
文献类型：
--
作者：
I. Kra
Teichmüller定理给出了一个K-拟共形映射将一个序四元组映射到第二个序四元组的充要条件。我们给出了一个简单的非计算证明的必要性部分。然后，我们刻画这样的极值映射，并因此获得一个新的公式的模函数，导致一个非常简单的推导已知的表达式的庞加莱度量的三次穿孔球。
Teichmüller’s theorem gives necessary and sufficient conditions for mapping one ordered quadruple by aK-quasiconformal map onto a second ordered quadruple. We give a simple non-computational proof of the necessity part. We then characterize such extremal mappings, and obtain as a consequence a new formula for the modular function, with leads to a very simple derivation of the known expression for the Poincaré metric on the thrice-punctured sphere.