Asymptotics of Weil–Petersson Geodesics I: Ending Laminations, Recurrence, and Flows
Asymptotics of Weil–Petersson Geodesics I: Ending Laminations, Recurrence, and Flows
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Weil-Petersson 测地线 I 的渐进线：结束叠层、循环和流动
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Y. Minsky
中科院分区：
文献类型：
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作者：
Jeffrey F. Brock;H. Masur;Y. Minsky
我们定义了 Weil-Petersson 测地射线的结束叠层。尽管 Weil-Petersson 度量 [Bro2] 缺乏自然的视觉边界，但这些末端叠层提供了一种有效的边界理论，可以对其大部分渐近 CAT(0) 几何结构进行编码。特别是，我们证明了循环到厚部分的全测量射线集的结束叠层定理（定理 1.1），并且我们证明了结束叠层的关联将循环射线的渐近线类嵌入到曲线复合体 $${\mathcal{C}(S)}$$ 的格罗莫夫边界中。作为一个应用，我们建立了韦尔-彼得森测地流的拓扑动力学基础，显示了闭合轨道的密度和拓扑传递性。
We define an ending lamination for a Weil–Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil–Petersson metric [Bro2], these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and we show that the association of an ending lamination embeds asymptote classes of recurrent rays into the Gromov-boundary of the curve complex $${\mathcal{C}(S)}$$. As an application, we establish fundamentals of the topological dynamics of the Weil–Petersson geodesic flow, showing density of closed orbits and topological transitivity.