K\"ahler manifolds with negative holomorphic sectional curvature, K\"ahler-Ricci flow approach

TL;DR

This paper provides a new proof connecting negative holomorphic sectional curvature with positive canonical bundles on compact K"ahler manifolds, using the K"ahler-Ricci flow approach.

Contribution

It offers an alternative proof of Wu-Yau and Tosatti-Yang's theorems through the application of the K"ahler-Ricci flow.

Findings

Established the link between negative holomorphic sectional curvature and positivity of canonical bundles.

Demonstrated the effectiveness of the K"ahler-Ricci flow in proving geometric curvature results.

Provided a new perspective on the relationship between curvature and algebraic properties of K"ahler manifolds.

Abstract

Recently, Wu-Yau and Tosatti-Yang established the connection between the negativity of holomorphic sectional curvatures and the positivity of canonical bundles for compact K\"ahler manifolds. In this short note, we give anothe proof of their theorems by using the K\"ahler-Ricci flow.