The Weyl functional, de Rham cohomology, and Kähler-Einstein metrics (Q1273517)

The main results of this paper are concerned with the problem of minimizing \({\mathcal W}_+\), the self-dual Weyl functional, over the space of metrics which are subject to a geometric constraint. Since \({\mathcal W}_+\) is conformally invariant, it is necessary that the constraint also is conformally invariant. For this reason a condition on the sign of the Yamabe invariant, \(Y(g)\), is imposed. When the underlying four-dimensional manifold satisfies some topological conditions, the author gives a sharp lower bound for \({\mathcal W}_+[g]\) for all metrics with \(Y(g)\) non-negative.