时球不变测度与n-生成Kleinian群
Horospherically invariant measures and finitely generated Kleinian groups
摘要：
设$ Γ< PSL_2(\mathbb{C}) $是一个Zerkiki稠密的生成Kleinian群.证明了$ PSL_2(\mathbb{C}) / Γ$上的所有Radon测度在次球面子群的作用下是遍历的和不变的，并且它们要么支持在一个闭次球面轨道上，要么关于测地标架流及其中心化子是准不变的.我们这样做是通过应用结果Landesberg和Lindenstrauss一起的基本成果理论的3流形，最显着的Tameness定理由Agol和Calegari-Gabai。
英文摘要：
Let $ Γ< PSL_2(\mathbb{C}) $ be a Zariski dense finitely generated Kleinian group. We show all Radon measures on $ PSL_2(\mathbb{C}) / Γ$ which are ergodic and invariant under the action of the horospherical subgroup are either supported on a single closed horospherical orbit or quasi-invariant with respect to the geodesic frame flow and its centralizer. We do this by applying a result of Landesberg and Lindenstrauss together with fundamental results in the theory of 3-manifolds, most notably the Tameness Theorem by Agol and Calegari-Gabai.
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