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

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