Deforming symplectomorphisms of complex projective spaces by the mean curvature flow

Abstract

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.

32 pages. Final version. To appear in Journal of Differential Geometry

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