  After a study of the Kobayashi metrics on certain scaled domains, we show the
stabilities of the infinitesimal Kobayashi metrics and the integrated distances
in different scaling processes. As an application, we prove that bounded
pseudo-convex domains of finite type where the Levi form of every boundary
point has corank one are Gromov hyperbolic with respect to the Kobayashi
metric. The results in this note generalize Zimmer's and Fiacchi's related
works on Gromov hyperbolicity of weakly pseudo-convex domains.

Complex Variables