Nonuniqueness of geodesics in infinite dimensional teichmuller spaces
Nonuniqueness of geodesics in infinite dimensional teichmuller spaces
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DOI：
10.1080/17476939108814483
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发表时间：
1991-05
影响因子：
0.9
通讯作者：
L. Zhong
中科院分区：
文献类型：
--
作者：
L. Zhong
构造了两个具有以下性质的极值Beltrami微分μ0和μ1: μ0和μ1表示泛Teichmuller空间中的同一个点P，而路径为tμ0和tμ1。0≤t≤1，表示将原点点与点p连接起来的不同测地线，这回答了E . P. Gardiner提出的无限维Teichmiiller空间中测地线唯一性的开放问题。此外，还证明了用这种方法可以得到无限多条连接两点的测地线。
Two extremal Beltrami differentials μ0 and μ1 with the following properties are constructed: μ0 and μ1 represent a same point P in the universal Teichmuller space, while the paths tμ0 and tμ1. 0 ≤ t ≤ 1, represent different geodesics joining the original point to the point P. This answers an open problem on the uniqueness of geodesics in infinite dimensional Teichmiiller spaces proposed by E P. Gardiner. Moreover, it is shown that one can get infinitely many geodesis joining two points in such a way.