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The famous pinching problem says that on a compact simply connected$n$-manifold if its sectional curvature satisfies $K_{min} > (1/4)K_{max} > 0$,then the manifold is homeomorphic to the sphere. In [8, problem 12], S. T. Yauproposed the following problem: If we replace $K_{max}$ by the scalarcurvature, can we deduce similar pinching theorems? In our present note we givean answer to this question in dimension $n = 4.$}

The scalar curvature and the biorthogonal curvature: A pinching problem