In manifolds with special holonomy, it is interesting to
study calibrated submanifolds, which are volume minimizer in their
homology classes. We study the calibrated submanifolds and mean
curvature flow in several famous local models of manifolds with
special holonomy. These model spaces are all total spaces of some
vector bundles, and the zero section is a calibrated submanifold. We
show that the zero section is the only compact minimal submanifold,
and is dynamically stable under the mean curvature flow. This is a
joint work with Mu-Tao Wang.