Frames of quasi-geodesics, visibility and geodesic loops

TL;DR

This paper characterizes the relationship between quasi-geodesic frames, visibility, and geodesic loops in bounded domains of complex space that are Kobayashi complete hyperbolic and Gromov hyperbolic.

Contribution

It introduces a new characterization using quasi-geodesic frames for visibility and geodesic loops in certain complex domains, linking geometric properties.

Findings

Characterization of visibility in terms of quasi-geodesic frames.

Existence criteria for geodesic loops in Kobayashi complete hyperbolic domains.

Connection between Gromov hyperbolicity and geodesic structures.

Abstract

In this paper we give a characterization in terms of ``quasi-geodesics frames' of visibility and existence of geodesic loops for bounded domains in $\mathbb C^d$ which are Kobayashi complete hyperbolic and Gromov hyperbolic.