论文标题
霍斯磷的措施和有限生成的克莱恩群
Horospherically invariant measures and finitely generated Kleinian groups
论文作者
论文摘要
令$γ<psl_2（\ mathbb {c}）$为zariski密集有限生成的kleinian组。我们显示了$ PSL_2（\ Mathbb {C}） /γ$的所有ra措施，它们在霍斯氏亚组的作用下是赤型和不变的，要么在单个封闭的horosperical轨道或quasi-Invariant上支持相对于地球框架流及其中心剂。我们通过应用Landesberg和Lindenstrauss的结果以及3个Manifolds理论的基本结果来做到这一点，最著名的是Agol和Calegari-Gabai的驯服定理。
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.
