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We introduce the notion of k-lower divergence for geodesic rays in CAT(0)spaces. Building on the work of Charney and Sultan we give variouscharacterizations of k-contracting geodesic rays using k-lower divergence andk-slim triangles. We also characterize k-contracting geodesic rays in CAT(0)cube complexes using sequences of well-separated hyperplanes.

Sublinearly Morse Geodesics in CAT(0) Spaces: Lower Divergence and Hyperplane Characterization