Global construction of pleating coordinates of Teichmuller spaces and its applications

我们估计了由X沿简单封闭测地线c通过θ接枝得到的黎曼曲面X和Y之间的Teichmuller距离。作为一个应用，我们估计了（1,1）型正则b群的共形边界和凸核边界之间的Teichmuller距离，其中一个给出了K=2猜想的反例。同时利用测地线长度函数，将2维和3维的Teichmuller空间实现为实射影空间中的凸多面体。

We estimate the Teichmuller distance between Riemann surfaces X and Y which is obtained from X byθ-grafting along a simple closed geodesic C. As anapplication we estimate the Teichmuller distance between the conformal boundary andthe convex core boundary of some regular b-groups of type (1,1) one of which gives acounterexample of K=2 conjecture. Also by means of geodesic length functions, werealize Teichmuller spaces of dimension 2 and 3 as convex polyhedron in real projective spaces.