  The goal of this article is to study the pinching problem proposed by S.-T.
Yau in 1990 replacing sectional curvature by one weaker condition on
biorthogonal curvature. Moreover, we classify 4-dimensional compact oriented
Riemannian manifolds with nonnegative biorthogonal curvature. In particular, we
obtain a partial answer to Yau Conjecture on pinching theorem for 4-dimensional
compact manifolds.
