Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity

This is the authors' abstract. We don't add key points for this paper.

In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying Gromov’s $4$ -point condition) while the intersection of any two metric balls therein does not either ‘look like’ a ball or has uniformly bounded eccentricity. This answers an open question posed by Chatterji and Niblo.