The parabolic Monge–Ampère equation on compact almost Hermitian manifolds

We prove the long time existence and uniqueness of solutions to the parabolic Monge–Ampère equation on compact almost Hermitian manifolds. We also show that the normalization of solution converges to a smooth function in {C^{\infty}} topology as {t\rightarrow\infty}. Up to scaling, the limit function is a solution of the Monge–Ampère equation. This gives a parabolic proof of existence of solutions to the Monge–Ampère equation on almost Hermitian manifolds.