Extremal length estimates and product regions in Teichm
Extremal length estimates and product regions in Teichm
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DOI：
10.1215/s0012-7094-96-08310-6
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发表时间：
1994-07
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影响因子：
--
通讯作者：
Y. Minsky
中科院分区：
文献类型：
--
作者：
Y. Minsky
本文研究了有限型曲面的Teichm-uller空间上的Teichm-uller度量，在曲面的内射性半径较小的区域内.主要结果是：在这类区域中，Teichm“uller度量在有界加性畸变下由低维空间乘积上的超度量逼近.在证明中的主要技术工具是使用基于其双曲测地线代表的几何形状的曲面中的曲线的极值长度的估计。
We study the Teichm\"uller metric on the Teichm\"uller space of a surface of finite type, in regions where the injectivity radius of the surface is small. The main result is that in such regions the Teichm\"uller metric is approximated up to bounded additive distortion by the sup metric on a product of lower dimensional spaces. The main technical tool in the proof is the use of estimates of extremal lengths of curves in a surface based on the geometry of their hyperbolic geodesic representatives.