In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality between Chern numbers of compact complex surfaces of general type. Its major interest is the way it restricts the possible topological types of the underlying real 4-manifold. It was proved independently by Shing-Tung Yau and Yoichi Miyaoka, after Antonius Van de Ven and Fedor Bogomolov proved weaker versions with the constant 3 replaced by 8 and 4.