Parabolic Flow for Generalized complex Monge-Amp\`ere type equations

TL;DR

This paper investigates a parabolic flow approach to solving generalized complex Monge-Ampère equations on Hermitian manifolds, establishing smooth estimates and convergence results.

Contribution

It introduces a new parabolic flow method for generalized complex Monge-Ampère equations and proves its smooth convergence on Hermitian manifolds.

Findings

Established a priori $C^ abla$ estimates for solutions.

Proved smooth convergence of the flow.

Extended techniques to generalized complex Monge-Ampère equations.

Abstract

We study the parabolic flow for generalized complex Monge-Amp\`ere type equations on closed Hermitian manifolds. We derive {\em a priori} $C^\infty$ estimates for normalized solutions, and then prove the $C^\infty$ convergence.