中文摘要：

在对数导数意义下,万有Teichmüller空间T_1可表示为无穷多个互不相交的连通分支的并集T1={∪θ∈（0,2π） Lθ}∪L,研究了该模型分支边界的几何性质,证明了L与Lθ的边界存在无穷多个公共点,同时还解决了关于一个分支中的点到另一分支中心距离上确界的公开问题．

英文摘要：

The model of the Universal Teichmiiller Space by the derivative of logarithm is the union of infinitely many disconnected components： T1={∪θ∈（0,2π） Lθ}∪L. In this paper, the geometric property of the boundary of T1 is investigated, and it is proved that for any θ∈（0,2π）δL and δLθ have infinitely many common points. In addition, an open problem about the supremum of the distance from the points of one component to the center of another component is solved.