An equation of Monge Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature


We formulate natural conformally invariant conditions on a $4$-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigenvalues of the Ricci tensor are positively pinched.


Sun-Yung A. Chang

Matthew J. Gursky

Paul C. Yang