Uniform perfectness of the limit sets of Kleinian groups
Uniform perfectness of the limit sets of Kleinian groups
复制标题
克莱因群极限集的一致完备性
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
T. Sugawa
中科院分区：
文献类型：
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作者：
T. Sugawa
在本文中，我们以定量的方式证明，如果商轨道折叠是 Lehner 型，即，如果其上可积全纯二次微分的空间连续包含在（双曲）有界群的空间中，则非初等克莱因群的极限集是一致完美的。该结果涵盖了群分析有限时的已知情况。作为应用，我们提出了这样一个克莱因群的极限集的豪斯多夫维数和不连续区域的平移长度的估计。还将给出几个例子。
In this note, we show, in a quantitative fashion, that the limit set of a non-elementary Kleinian group is uniformly perfect if the quotient orbifold is of Lehner type, i.e., if the space of integrable holomorphic quadratic differentials on it is continuously contained in the space of (hyperbolically) bounded ones. This result covers the known case when the group is analytically finite. As applications, we present estimates of the Hausdorff dimension of the limit set and the translation lengths in the region of discontinuity for such a Kleinian group. Several examples will also be given.