#### Volume 22, issue 3 (2022)

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Sublinearly Morse geodesics in CAT(0) spaces: lower divergence and hyperplane characterization

### Devin Murray, Yulan Qing and Abdul Zalloum

Algebraic & Geometric Topology 22 (2022) 1337–1374
##### Abstract

We introduce the notion of $\kappa$–lower divergence for geodesic rays in CAT(0) spaces. Building on work of Charney and Sultan, we give various characterizations of $\kappa$–contracting geodesic rays using $\kappa$–lower divergence and $\kappa$–slim triangles. We also characterize $\kappa$–contracting geodesic rays in CAT(0) cube complexes using sequences of well-separated hyperplanes.

##### Keywords
boundary, CAT(0) cube complex, sublinearly Morse
Primary: 57M60