  Let $h$ be the planar Gaussian free field and let $D_h$ be a supercritical
Liouville quantum gravity (LQG) metric associated with $h$. Such metrics arise
as subsequential scaling limits of supercritical Liouville first passage
percolation (Ding-Gwynne, 2020) and correspond to values of the matter central
charge $\mathbf{c}_{\mathrm M} \in (1,25)$. We show that a.s. the boundary of
each complementary connected component of a $D_h$-metric ball is a Jordan curve
and is compact and finite-dimensional with respect to $D_h$. This is in
contrast to the \emph{whole} boundary of the $D_h$-metric ball, which is
non-compact and infinite-dimensional with respect to $D_h$ (Pfeffer, 2021).
Using our regularity results for boundaries of complementary connected
components of $D_h$-metric balls, we extend the confluence of geodesics results
of Gwynne-Miller (2019) to the case of supercritical Liouville quantum gravity.
These results show that two $D_h$-geodesics with the same starting point and
different target points coincide for a non-trivial initial time interval.
