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

Differential Geometry;Analysis of PDEs