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 ∞ topology as t → ∞. 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.
ASJC Scopus subject areas
- Applied Mathematics