AI 中文总结
本文针对一般收敛群作用，引入轨道一致度量概念，刻画几何无限性，推广了Gromov双曲空间上作用的对应结果。
AI 中文摘要
针对Gromov双曲空间上的作用，已有用较弱条件刻画几何有限性的两种方法。本文针对一般收敛群作用建立了类似的刻画，为此引入轨道一致度量的概念。我们证明，一个点要么是锥形极限点，要么是有界抛物极限点，当且仅当其轨道相对于轨道一致度量是离散的。由此，我们通过非锥形极限点集合的不可数性刻画几何无限性，还通过双曲元素逃逸序列的存在性进一步刻画几何无限性，从而推广了Gromov双曲空间上作用的对应结果。
英文摘要
Two characterizations of geometric finiteness in terms of weaker conditions are known for actions on Gromov hyperbolic spaces. In this paper, we establish analogous characterizations for general convergence group actions. To this end, we introduce the notion of an orbit uniform metric. We prove that a point is either conical or bounded parabolic if and only if its orbit is discrete with respect to an orbit uniform metric. As a consequence, we characterize geometric infiniteness in terms of the uncountability of the set of non-conical limit points. We further characterize geometric infiniteness by the existence of escaping sequences of hyperbolic elements, thereby extending the corresponding result for actions on Gromov hyperbolic spaces.
Comments18 pages, 1 figure
