  In this paper, we first prove that any power quasi-symmetry of two metric
spaces induces a rough quasi-isometry between their infinite hyperbolic cones.
Second, we prove that for a complete metric space $Z$, there exists a point
$\omega$ in the Gromov boundary of its infinite hyperbolic cone such that $Z$
can be seen as the Gromov boundary relative to $\omega$ of its infinite
hyperbolic cone. Third, we prove that for a visual Gromov hyperbolic metric
space $X$ and a Gromov boundary point $\omega$, $X$ is roughly similar to the
infinite hyperbolic cone of its Gromov boundary relative to $\omega$. These are
the generalizations of Theorem 7.4, Theorem 8.1 and Theorem 8.2 in [3] since
the underlying spaces are not assumed to be bounded and the hyperbolic cones
are infinite.
