Given a path of almost-K?hler metrics compatible with a fixed symplectic form on a compact 4-manifold such that at time zero the almost-K?hler metric is an extremal K?hler one, we prove, for a short time and under a certain hypothesis, the existence of a smooth family of extremal almost-K?hler metrics compatible with the same symplectic form, such that at each time the induced almost-complex structure is diffeomorphic to the one induced by the path.
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