Isotriviality of smooth families of varieties of general type

In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the generalized Kebekus-Kov'acs conjecture \cite[Conjecture 1.1]{WW19}, for smooth families of general type varieties as well as log smooth families of log canonical pairs of log general type, assuming the existence of relative good minimal models.