DOCUMENTA MATHEMATICA, Vol. 22 (2017), 1193-1224

Goulnara N. Arzhantseva, Christopher H. Cashen, Dominik Gruber, and David Hume

Characterizations of Morse Quasi-Geodesics via Superlinear Divergence and Sublinear Contraction

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.

2010 Mathematics Subject Classification: Primary: 20F65; Secondary: 20F67.

Keywords and Phrases: Morse quasi-geodesic, contracting projection, superlinear divergence, geodesic image theorem.

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