The coarse separation characterization of non-elementary hyperbolic groups

Let $G$ be a non-elementary hyperbolic group. A subspace has subexponential growth if its growth function is subexponential, and $G$ is coarsely separable by subspaces of subexponential growth if it admits the corresponding coarse separation property using such subspaces. Coarse separation characterization. $G$ is coarsely separable by subspaces of subexponential growth if and only if it splits over a two-ended group. This conjecture proposes a characterization of the hyperbolic groups in this class; the article establishes membership for a large class of hyperbolic groups, while the general equivalence remains open.