本项目主要研究以下内容：（1）在Teichmüller空间里引入角度概念，并利用它来研究空间凸性及测地盘等问题。我们也关心T0子空间的测地线问题。（2）分别考察渐进Teichmüller空间中本性点与非本性点，以图弄清楚渐进Teichmüller空间的测地几何性态。（3）考察渐进Bers空间与渐进Teichmüller空间之间的联系，借助于最近由Markovic解决的Schoen猜想来研究拟共形调和映射的渐进边界行为。

The main aim of this project is to study the geometry in Teichmüller spaces and asymptotic Teichmüller spaces. It contains three subjects. (1) We introduce the conception of angle in Teichmüller spaces and use it to study the convexity and geodesic disks. We also consider the geodesic problem in the T0-subspace. (2) We investigate the substantial points and non-substantial points in asymptotic Teichmüller spaces separately and try to reveal the configuration of geodesic geometry in asymptotic Teichmüller spaces. (3) We will investigate the relation between the asymptotic Bers space and the asymptotic Teichmüller space. With the help of the proof of Schoen's conjecture by Markovic, we explore the asymptotic boundary behavior of quasiconformal harmonic maps.