Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction

Abstract

We introduce and begin a systematic study of sublinearly contracting projections. We give two characterizations of Morse quasi-geodesics in an arbitrary geodesic metric space. One is that they are sublinearly contracting; the other is that they have completely superlinear divergence. We give a further characterization of sublinearly contracting projections in terms of projections of geodesic segments.

24 pages, 5 figures. v2: 22 pages, 5 figures. Correction in proof of Thm 7.1. Proof of Prop 4.2 revised for improved clarity. Other minor changes per referee comments. To appear in Documenta Mathematica