  We identify a strong stability condition on minimal submanifolds that implies
uniqueness and dynamical stability properties. In particular, we prove a
uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature
flow for minimal submanifolds that satisfy this condition. The latter theorem
states that the mean curvature flow of any other submanifold in a C^1
neighborhood of such a minimal submanifold exists for all time, and converges
exponentially to the minimal one. This extends our previous uniqueness and
stability theorem [arXiv:1605.03645] which applies only to calibrated
submanifolds of special holonomy ambient manifolds.
