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

Abstract

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 various characterizations of k-contracting geodesic rays using k-lower divergence and k-slim triangles. We also characterize k-contracting geodesic rays in CAT(0) cube complexes using sequences of well-separated hyperplanes.

30 pages

References in corpus (2)

• Large facing tuples and a strengthened sector lemma
• An embedding of the Morse boundary in the Martin boundary