论文标题
sublrinear bilipschitz等效性和sublerearlie Morse边界
Sublinear biLipschitz equivalence and sublinearly Morse boundaries
论文作者
论文摘要
度量空间之间的sublinear bilipschitz等价（SBE）是从一个空间到另一个空间的地图，它扭曲了有界的乘法常数和sublinear添加误差。鉴于任何额线功能$κ$，$κ$ - 摩尔斯边界均定义为所有地球适当的度量空间，为准地理射线的准中性不变且可迁移的拓扑空间。在本文中，我们证明，在合适的SBE下，$κ$ -Morse的边界是不变的。证据中的一种工具是使用sublinear射线，即半线的sublinear bilispchitz嵌入，从而概括了准晶状射线。作为一种应用，我们区分了一对由Behrstock提出的右角Coxeter组，直至Sublrinear Bilipschitz等价。我们还表明，在轻度的假设下，可计数组的通用随机步行是均方根射线。
A sublinear biLipschitz equivalence (SBE) between metric spaces is a map from one space to another that distorts distances with bounded multiplicative constants and sublinear additive error. Given any sublinear function $κ$, $κ$-Morse boundaries are defined for all geodesic proper metric spaces as a quasi-isometrically invariant and metrizable topological space of quasi-geodesic rays. In this paper, we prove that $κ$-Morse boundaries of proper geodesic metric spaces are invariant under suitable SBEs. A tool in the proof is the use of sublinear rays, that is, sublinear bilispchitz embeddings of the half line, generalizing quasi-geodesic rays. As an application we distinguish a pair of right-angled Coxeter groups brought up by Behrstock up to sublinear biLipschitz equivalence. We also show that under mild assumptions, generic random walks on countable groups are sublinear rays.
