A note on compact Kähler manifolds with quasi-negative holomorphic sectional curvature

Abstract

A compact Kähler manifold with quasi-negative holomorphic sectional curvature must have ample canonical bundle. This was conjectured by Wu-Yau and is recently proved by the continuity method. In this note, we will give an alternative proof of this result by using the Kähler-Ricci flow.