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 theâ€¦ (More)

The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds,â€¦ (More)

In this paper we study the problem of finding a conformal metric with the property that the k-th elementary symmetric polynomial of the eigenvalues of its Weyl-Schouten tensor is constant. A newâ€¦ (More)

We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functionsâ€¦ (More)

We present a conformal deformation involving a fully nonlinear equation in dimension 4, starting with positive scalar curvature. Assuming a certain conformal invariant is positive, one may deformâ€¦ (More)

Let (M, g) be a compact oriented four-dimensional Einstein manifold. If M has positive intersection form andg has non-negative sectional curvature, we show that, up to rescaling and isometry,(M, g)â€¦ (More)

We define a generalization of convex functions, which we call Î´-convex functions, and show they must satisfy interior HÃ¶lder and W 1,p estimates. As an application, we consider solutions of a certainâ€¦ (More)