Longtime existence of K\"ahler Ricci flow and holomorphic sectional curvature

TL;DR

This paper establishes criteria for the long-term existence of the K"ahler Ricci flow, generalizes Wu-Yau's results on K"ahler Einstein metrics to unbounded curvature cases, and proves their uniqueness under negative scalar curvature.

Contribution

It provides new existence criteria for the K"ahler Ricci flow and extends the understanding of K"ahler Einstein metrics beyond bounded curvature scenarios.

Findings

Longtime existence criteria for K"ahler Ricci flow.

Generalization of Wu-Yau's results to unbounded curvature.

Uniqueness of K"ahler Einstein metrics with negative scalar curvature.

Abstract

In this work, we obtain a existence criteria for the longtime K\"ahler Ricci flow solution. Using the existence result, we generalize a result by Wu-Yau on the existence of K\"ahler Einstein metric to the case with possibly unbounded curvature. Moreover, the K\"ahler Einstein metric with negative scalar curvture must be unique up to scaling.