论文标题
缔约边界上的等效拓扑
Equivalent Topologies on the Contracting Boundary
论文作者
论文摘要
适当的大地测量空间的收缩边界概括了双曲线空间的Gromov边界。它包括将大地测量学签约到有限的Hausdorff距离。 Gromov边界的另一个概括是$κ$ -Morse边界，具有sublinear函数$κ$。这两个概括基于Gromov双曲线空间中大地测量学特征的不同特征模拟了Gromov边界。人们怀疑$κ$ - 摩尔斯边界包含收缩边界。我们将证明这一猜想：当$κ= 1 $是恒定函数时，1摩尔边界和收缩边界等于拓扑空间。
The contracting boundary of a proper geodesic metric space generalizes the Gromov boundary of a hyperbolic space. It consists of contracting geodesics up to bounded Hausdorff distances. Another generalization of the Gromov boundary is the $κ$-Morse boundary with a sublinear function $κ$. The two generalizations model the Gromov boundary based on different characteristics of geodesics in Gromov hyperbolic spaces. It was suspected that the $κ$-Morse boundary contains the contracting boundary. We will prove this conjecture: when $κ=1$ is the constant function, the 1-Morse boundary and the contracting boundary are equivalent as topological spaces.
