The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

Abstract

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 $t\to \infty$. 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.

25 pages

References in corpus (1)

• Taming symplectic forms and the Calabi-Yau equation

Cited by in corpus (1)

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