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.

Full text: dvi.gz 69 k, dvi 240 k, ps.gz 466 k, pdf 384 k.

Home Page of DOCUMENTA MATHEMATICA