具有一维边界面的凸余紧群
Convex co-compact groups with one dimensional boundary faces
AI总结：
本文研究射影线性群的凸余紧子群，利用理想边界面维数和粗Hilbert维数，刻画了此类群及朴素凸余紧子群为字双曲或相对双曲的条件。
摘要：
本文考虑射影线性群的凸余紧子群。我们证明，这样的群相对于秩为2的拟阿贝尔子群集合是相对双曲的，当且仅当理想边界中的每个开面维数至多为1。我们还引入了凸集子集的“粗Hilbert维数”，并用它刻画了朴素凸余紧子群何时是字双曲的，或相对于秩为2的拟阿贝尔子群集合是相对双曲的。
英文摘要：
In this paper we consider convex co-compact subgroups of the projective linear group. We prove that such a group is relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two if and only if each open face in the ideal boundary has dimension at most one. We also introduce the "coarse Hilbert dimension" of a subset of a convex set and use it to characterize when a naive convex co-compact subgroup is word hyperbolic or relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
