Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity (Q6634407)

In the interesting paper under review, the authors give examples of Gromov-hyperbolic non-quasi-geodesic metric spaces in which the intersection of any two metric balls does not either ``look like'' a ball or has uniformly bounded eccentricity. More precisely, they prove that there exists a non-quasi-geodesic Gromov-hyperbolic metric space which does not satisfy either of the following two properties: (i) The quasi-ball property, which says that the intersection of any two metric balls is at a uniformly bounded Hausdorff distance from a ball; (ii) the bounded eccentricity property, saying that the intersection of any two metric balls has uniformly bounded eccentricity, a notion introduced by \textit{I. Chatterji} and \textit{G. A. Niblo} [Groups Geom. Dyn. 1, No. 3, 281--299 (2007; Zbl 1137.20036)]. Chatterji and Niblo showed in this paper that in a geodesic Gromov-hyperbolic metric space, the intersection of any two metric balls is at uniformly bounded Hausdorff distance from a ball.The result of the paper under review answers an open question posed by Chatterji and Niblo in the paper mentioned.