Scalar curvature and connected sums of self-dual 4-manifolds

Under a reasonable vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-manifolds is again self-dual. Here we prove that the same result can be extended to the positive scalar curvature case. This is an analogue of the classical theorem of Gromov-Lawson and Schoen-Yau in the self-dual category. The proof is based on twistor theory.