Deforming symplectomorphism of certain irreducible Hermitian symmetric spaces of compact type by mean curvature flow

In this paper, we generalize Medos-Wang's arguments and results on the mean curvature flow deformations of symplectomorphisms of $\CP^n$ in \cite{MeWa} to complex Grassmann manifold $G(n, n+m;\C)$ and compact totally geodesic K\"ahler-Einstein submanifolds of $G(n, 2n;\C)$ such as irreducible Hermitian symmetric spaces $SO(2n)/U(n)$ and $Sp(n)/U(n)$ (in the terminology of \cite[p. 518]{He}). We also give an abstract result and discuss the case of complex tori.