2 citations · 3 across the 3 of their papers we have counts for
4 papers · 1 filter
Convexity and singularities of curvature equations in conformal geometry
Matthew Gursky, Jeff Viaclovsky
We define a generalization of convex functions, which we call -convex functions, and show they must satisfy interior Hölder and estimates. As an application, we consid…
An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature
Sun-Yung A. Chang, Matthew J. Gursky, Paul C. Yang
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…
A conformally invariant sphere theorem in four dimensions
S. Y. A Chang, Matthew J. Gursky, Paul Yang
In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 ineq…
On Einstein Manifolds of Positive Sectional Curvature
Matthew Gursky, Claude LeBrun
Let (M,g) be a compact oriented Einstein 4-manifold. If M has positive intersection form and g has non-negative sectional curvature, we show that, up to rescaling and isometry, (M,…