On Completing Triangles in Teichmuller Space
On Completing Triangles in Teichmuller Space
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作者：
G. Yao
设T（）是泛Teichmüuller空间. T（）中的三个点（f）、（1）和（h）被称为构成一个完备三角形，如果每对点都有一条唯一的测地线连接它们。最近，Z. Zhou和L. Liu构造了两个Strebel点（f）和（1），使得（id），（f）和（1）形成一个不完全三角形。在他们的建设计算是冗长和复杂的。本文证明了它们的结果可以用简单得多的方法得到。事实上，目前的Teichmüuller空间理论使我们能够给出更多关于无限维Teichmüuller空间中三角形的信息。我们的方法是自包含的，并适用于一般的Teichmüuller空间。
Let T( ) be the universal Teichm ¨ uller space. Three points ( f ), (1) and (h) in T( ) are called to form a completing triangle if each pair of them has a unique geodesic joining them. Recently, Z. Zhou and L. Liu constructed two Strebel points ( f ) and (1) such that (id), ( f ) and (1) form a non-completing triangle. The computation in their construction is lengthy and complicated. In this note, it is shown that their results can be obtained in much simpler a way. Indeed, the current theory of Teichm ¨ uller spaces allows us to give more information on triangles in an infinite-dimensional Teichm ¨ uller space. Our method is self-contained and applies for general Teichm ¨ uller spaces.