Convergence of the parabolic complex Monge-Amp\`ere equation on compact Hermitian manifolds

TL;DR

This paper proves smooth convergence of solutions to the parabolic complex Monge-Ampère equation on compact Hermitian manifolds, offering a new parabolic approach to a recent result by Tosatti and Weinkove.

Contribution

It introduces a parabolic proof of convergence for the complex Monge-Ampère equation on Hermitian manifolds, extending previous results.

Findings

Proves $C^ ablafty$ convergence of solutions

Provides a new parabolic proof of existing results

Extends understanding of complex Monge-Ampère equations on Hermitian manifolds

Abstract

We prove $C^\infty$ convergence for suitably normalized solutions of the parabolic complex Monge-Amp\`ere equation on compact Hermitian manifolds. This provides a parabolic proof of a recent result of Tosatti and Weinkove.