Deforming symplectomorphisms of complex projective spaces by the mean curvature flow

We apply the mean curvature flow to deform symplectomorphisms of ${\mathbb{C}\mathbb{P}}^n$. In particular, we prove that, for each dimension n, there exists a constant $\mathrm{\Lambda }$, explicitly computable, such that any $\mathrm{\Lambda }$-pinched symplectomorphism of ${\mathbb{C}\mathbb{P}}^n$ is symplectically isotopic to a biholomorphic isometry.