  In a previous paper (Kato 2017a) we have examined how the self-trapping of
g-mode oscillations in geometrically thin relativistic disks is affected by the
presence of uniform vertical magnetic fields. Disks considered are isothermal
in the vertical direction and are truncated at a certain height by presence of
hot corona. After a correction of simple analytical error, we showed (Kato
2017b) that the self-trapping of axisymmetric g-mode oscillations in
non-magnetized disks is destroyed by weak magnetic fields as Fu and Lai (2009)
showed. In this paper, however, we re-examine the same problem by imposing a
different more relevant boundary condition on the disk-corona surface and find
that the self-trapping of axisymmetric g-mode oscillations seems to still exist
like the case of non-magnetized disks.
