论文标题
球形化及其在Gromov双曲空间中的应用
Sphericalization with its applications in Gromov hyperbolic spaces
论文作者
论文摘要
在本文中，我们研究了球形化在Gromov双曲线度量空间中的某些应用。我们首先表明，双曲线空间的Gromov边界上有关两类指标的双重属性是重合的。接下来，我们通过度量空间球形化获得了无界Gromov双曲线域的表征。最后，我们研究了Gromov边界和内部度量边界之间的Gromov双曲线$φ$ - 均匀域的拓扑当量。
In this paper, we study certain applications of sphericalization in Gromov hyperbolic metric spaces. We first show that the doubling property regarding two classes of metrics on the Gromov boundary of hyperbolic spaces are coincided. Next, we obtain a characterization of unbounded Gromov hyperbolic domains via metric spaces sphericalization. Finally, we investigate the topological equivalence of Gromov hyperbolic $φ$-uniform domains between the Gromov boundary and the inner metric boundary.
