Measurable Rigidity for Kleinian groups
Measurable Rigidity for Kleinian groups
复制标题
克莱因群的可测量刚性
DOI：
10.1017/etds.2015.15
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Ken'ichi Ohshika
中科院分区：
文献类型：
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作者：
Woojin Jeon;Ken'ichi Ohshika
设G， H为两个具有同胚商H3/G和H3/ H的Kleinian群。我们假设G是散度型，并考虑G和H的Patterson-Sullivan测度。Sullivan和Tukia的可测刚性定理指出，从G的极限集G到H的极限集G的可测且本质上直接可测的等变边界映射，要么是Möbius变换的限制，要么是完全奇异的。在本文中，我们将证明这样的n总是存在的。事实上，我们将构建
Let G, H be two Kleinian groups with homeomorphic quotients H3/G and H 3/H. We assume that G is of divergence type, and consider the Patterson–Sullivan measures of G and H. The measurable rigidity theorem by Sullivan and Tukia says that a measurable and essentially directly measurable equivariant boundary map̂kfrom the limit set G of G to that of H is either the restriction of a Möbius transformation or totally singular. In this paper, we shall show that such ̂kalways exists. In fact, we shall construct