On Geodesics in Asymptotic Universal Teichmüller Space
On Geodesics in Asymptotic Universal Teichmüller Space
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DOI：
10.1017/s0013091515000449
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发表时间：
2016-01
影响因子：
0.7
通讯作者：
Zhou Ze-min;Chen Jixiu
中科院分区：
文献类型：
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作者：
Zhou Ze-min;Chen Jixiu
设AT(Δ)是渐近泛Teichmüler空间，可看作是所有渐近Teichmüler等价类[[μ]]的空间。证明了如果μ在AT(Δ)和hp([[μ]])<；h([[μ]])中是渐近极值的，则Δ的某个边界点p有无穷多条测地线连接[[0]]和[[μ]]在AT(Δ).作为推论，给出了AT(Δ)中的复伸张唯一极值的一个必要条件。
Abstract Let AT(Δ) be the asymptotic universal Teichmüller space, viewed as the space of all asymptotic Teichmüller equivalence classes [[μ]]. We show that if μ is asymptotically extremal in AT(Δ) and h p ([[μ]]) < h([[μ]]) for some boundary point p of Δ, then there are infinitely many geodesics joining [[0]] and [[μ]] in AT(Δ). As a corollary, a necessary condition for a complex dilatation to be uniquely extremal in AT(Δ) is given.