Visual maps between coarsely convex spaces

TL;DR

This paper extends the understanding of boundary maps from Gromov hyperbolic spaces to the broader class of coarsely convex spaces, revealing new insights into their geometric and boundary relationships.

Contribution

It generalizes boundary map results from Gromov hyperbolic spaces to coarsely convex spaces, broadening the scope of coarse geometric analysis.

Findings

Generalization of boundary map theory to coarsely convex spaces

Establishment of conditions for boundary maps in coarsely convex spaces

Connections between coarse embeddings and boundary topologies

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.