Regularity of Kleinian limit sets and Patterson-Sullivan measures
Regularity of Kleinian limit sets and Patterson-Sullivan measures
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克莱因极限集的正则性和帕特森-沙利文测度
DOI：
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发表时间：
2017
影响因子：
1.3
通讯作者：
J. Fraser
中科院分区：
文献类型：
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作者：
J. Fraser
我们考虑几个（相关）的几何正则性的概念的背景下，极限集的几何有限Kleinian群和相关的帕特森-沙利文措施。我们开始计算的帕特森-沙利文措施，这涉及到控制同心球的相对测量的上，下规则性尺寸。然后，我们计算的Assouad和较低的尺寸的极限集，这涉及到控制本地加倍性能。不同于豪斯多夫，包装，盒计数尺寸，我们表明，Assouad和较低的尺寸不一定由庞加莱指数。
We consider several (related) notions of geometric regularity in the context of limit sets of geometrically finite Kleinian groups and associated Patterson-Sullivan measures. We begin by computing the upper and lower regularity dimensions of the Patterson-Sullivan measure, which involves controlling the relative measure of concentric balls. We then compute the Assouad and lower dimensions of the limit set, which involves controlling local doubling properties. Unlike the Hausdorff, packing, and box-counting dimensions, we show that the Assouad and lower dimensions are not necessarily given by the Poincare exponent.