Projective structures, grafting, and measured laminations
Projective structures, grafting, and measured laminations
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投影结构、嫁接和测量叠层
DOI：
10.2140/gt.2008.12.351
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Michael Wolf
中科院分区：
文献类型：
--
作者：
D. Dumas;Michael Wolf
我们发现，嫁接任何固定的双曲曲面定义了一个同胚从空间的测量叠层Teichmuller空间，补充的结果Scannell-Wolf嫁接固定的叠层。这一结果被用来研究复解析坐标系和几何坐标系之间的关系，为空间的复射影（$\CP^1$）结构的表面上。
我们还研究了Teichmuller空间中与嫁接坐标相关的射线，获得极值和双曲长度函数及其导数的估计，沿着这些嫁接射线。
We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems for the space of complex projective ($\CP^1$) structures on a surface.
We also study the rays in Teichmuller space associated to the grafting coordinates, obtaining estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays.