研究背景是单复变函数论中的拟共形映射与Teichmuller空间理论，与低维拓扑、复动力系统、微分几何、数学物理等紧密联系。研究与万有Teichmuller空间上的Weil-Petersson度量有关，目的是刻画万有Teichmuller空间在Weil-Petersson度量下包含零点的连通分支及研究其几何拓扑性质。. 万有Teichmuller空间有几种等价定义模型，主要目标是从边界函数模型刻画这一子空间，也就是刻画一类特殊的单位圆周拟对称同胚。拟采取的方法主要从两个角度：单位圆周上四点对交比的偏差以及单位圆周同胚的广义Fourier系数。

The research is based on the theory of quasiconformal mapping and Teichmuller space, which is connected with low-dimensional topology,complex dynamics, differential geometry and mathematical physics. The research is about the Weil-Petersson metric on universal Teichmuller space, and the aim is to characterize the connected component containing the zero of universal Teichmuller space, under Weil-Petersson metric, and to research its topological and geometrical properties.. Universal Teichmuller space has several equivalent definitions. The main aim is to characterize the subspace in the boudary value model, that is, to characterize a special kind of quasisymmetric homeomorphism of the unit circle. The approach is from the following two: the distortion of the cross-ratio of quadruples on the unit circle and the generalized Fourier coefficients of homeomorphism of the unit circle.