The $L^{\infty}$ estimate for parabolic complex Monge-Amp\`ere equations

TL;DR

This paper extends the $L^{ abla}$ estimate for Kähler-Ricci flows under weaker assumptions, broadening its applicability to various geometric contexts.

Contribution

It introduces a new approach to derive $L^{ abla}$ estimates for parabolic complex Monge-Ampère equations with less restrictive conditions.

Findings

Established $L^{ abla}$ estimates under weaker assumptions

Extended techniques to diverse geometric backgrounds

Enhanced understanding of Kähler-Ricci flow behavior

Abstract

Following the recent development by Guo-Phong-Tong and Chen-Cheng, we derived the $L^{\infty}$ estimate for K\"ahler-Ricci flows under a weaker assumption. The technique also extends to more general cases coming from different geometric backgrounds.