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

TL;DR

This paper extends the study of mean curvature flow deformations of symplectomorphisms from complex projective spaces to more general Hermitian symmetric spaces, providing new results on their geometric evolution.

Contribution

It generalizes existing results on symplectomorphism deformations under mean curvature flow to complex Grassmannians and certain Hermitian symmetric spaces, broadening the scope of geometric flow analysis.

Findings

Mean curvature flow deforms symplectomorphisms on new classes of spaces.

Results include convergence properties and stability analysis.

Discussion of the case for complex tori.

Abstract

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.