Visual maps between coarsely convex spaces

Abstract

The class of coarsely convex spaces is a coarse geometric analogue of the class of nonpositively curved Riemannian manifolds. It includes Gromov hyperbolic spaces, CAT(0) spaces, proper injective metric spaces and systolic complexes. It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces induce topological embeddings of their boundaries. Dydak and Virk studied maps between Gromov hyperbolic spaces which induce continuous maps between their boundaries. In this paper, we generalize their work to maps between coarsely convex spaces.