具有极限集的实双曲空间中的凸紧群

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2026-03-27 DOI:10.1112/blms.70319

Sami Douba, Gye-Seon Lee, Ludovic Marquis, Lorenzo Ruffoni

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引用次数: 0

摘要

我们给出了具有极限集的实双曲空间等距群的凸紧子群的两个例子：一个是由h4 $\mathbb {H}^4$的50个反射生成的，另一个是由h6 $\mathbb {H}^6$的21阶旋转和反射生成的。对于每一种情况，我们也在门格尔曲线上定位了具有极限集的凸紧子群。

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Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere

We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by 50 reflections of $H^{4}$ , and the other by a rotation of order 21 and a reflection of $H^{6}$ . For each of them, we also locate convex cocompact subgroups with limit set a Menger curve.