Sublinearly Morse boundary of CAT(0) admissible groups

Pub Date : 2024-01-15 DOI:10.1515/jgth-2023-0145

Hoang Thanh Nguyen, Yulan Qing

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引用次数: 0

Abstract

We show that if 𝐺 is an admissible group acting geometrically on a CAT ⁡ ( 0 )

\operatorname{CAT}(0)

space 𝑋, then 𝐺 is a hierarchically hyperbolic space and its 𝜅-Morse boundary ( ∂ κ G , ν )

(\partial_{\kappa}G,\nu)

is a model for the Poisson boundary of ( G , μ )

(G,\mu)

, where 𝜈 is the hitting measure associated to the random walk driven by 𝜇.

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CAT(0)可接纳群的次线性莫尔斯边界

我们证明，如果𝐺 是一个几何作用于 CAT ( 0 ) \operatorname{CAT}(0) 空间 𝑋 的可容许群，那么𝐺 是一个层次双曲空间，它的𝜅-Morse 边界 ( ∂ κ G 、ν ) (\partial_{k\appa}G,\nu) 是 ( G , μ ) (G,\mu) 的泊松边界模型，其中 𝜈 是与𝜇驱动的随机漫步相关的命中率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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