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

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