Research on the complex structure on Teichmuller space and the deformation space of Kleinian groups

在这期间，我研究了Teichmuller空间的几何。得到了Teichmuller空间的极值长度几何中的交数。作为应用，我们给出了Royden-Earle-Kra-Markovic-Ivanov的结果"除少数情况外，Teichmuller空间上的等距群与扩张映射类群重合”和Masur-Wolf定理" Teichmuller空间不是Gromov-双曲”的另一种证明.利用Gromov积的渐近性质，得到了Teichmuller空间中全纯圆盘的一个刚性定理。这是Thurston理论在Teichmuller空间复结构研究中的一个应用。

In this period, I study the geometry of Teichmuller space. I obtain the intersection number in extremal length geometry of Teichmuller space. As applications, we have an alternative proofs of Royden-Earle-Kra-Markovic-Ivanov's result ``Except for few cases, the isometry group on Teichmuller space coincides with the extended mapping class group", and Masur-Wolf's theorem ``Teichmuller space is not Gromov-hyperbolic". I also obtain a rigidity theorem of holomorphic disks in Teichmuller space by using the asymptotic behavior of the Gromov product. This is an application of our Thurston theory to the study of the complex structure on Teichmuller space.