The Weyl Functional, de Rham Cohomology, and Kahler-Einstein Metrics

Conformal Metrics with Constant Q-Curvature

“…Indeed some results in this spirit were obtained by Gursky in [34] (see also [33]). If a manifold of non-negative Yamabe class Y (g) satisfies also k P ≥ 0, then ker P g consists only of the constant functions and P g ≥ 0, namely P g is a non-negative operator.…”

On the topology of conformally compact Einstein 4-manifolds

“…We remark that this implies in view of the formula (0.1) that χ(X) > 0. In fact we have a stronger consequence according to the first vanishing theorem of Gursky [Gu2]:…”

Conformal invariants and partial differential equations

“…This understanding of the relation between the renormalized volume and the integral in the Chern-Gauss-Bonnet formula also allows us to translate some of the results in ( [59], [26], [28]) from compact 4-manifolds without boundary to the setting of conformal compact Einstein 4-manifolds. A crucial step in the proof of the theorem above is an earlier result by J. Qing ( [91]), which builds upon some earlier estimates of J. Lee [73] on the subject.…”