On length spectrum metrics and weak metrics on Teichmueller spaces of surfaces with boundary
On length spectrum metrics and weak metrics on Teichmueller spaces of surfaces with boundary
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DOI：
10.5186/aasfm.2010.3515
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发表时间：
2009-03
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影响因子：
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通讯作者：
Li-Xing Liu;A. Papadopoulos;W. Su;G. Th'eret
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作者：
Li-Xing Liu;A. Papadopoulos;W. Su;G. Th'eret
定义并研究了具有边界的拓扑有限型曲面的Teichmueller空间上的度量和弱度量。这些度量和弱度量与简单闭合曲线和适当嵌入曲面中的弧的双曲长度谱相关联。我们给出了Teichmueller空间的区域，我们称之为$\varepsilon_0 $-相对$\varepsilon_0\geq\n>0$厚的部分}之间的比较定义的度量。
We define and study metrics and weak metrics on the Teichmueller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmueller space which we call $\varepsilon_0$-relative $\epsilon$-thick parts} for $\epsilon >0$ and $\varepsilon_0\geq \epsilon>0$.