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

TL;DR

This paper characterizes Morse quasi-geodesics in geodesic metric spaces using superlinear divergence and sublinear contraction, providing new insights into their geometric properties.

Contribution

It introduces and systematically studies sublinearly contracting projections, offering two novel characterizations of Morse quasi-geodesics based on divergence and contraction.

Findings

Morse quasi-geodesics are characterized by sublinear contraction.

They have completely superlinear divergence.

Projections of geodesic segments relate to 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.