Curvature in the Balance: The Weyl Functional and Scalar Curvature of 4-Manifolds

Abstract

The infimum of the Weyl functional is shown to be surprisingly small on many compact 4-manifolds that admit positive-scalar-curvature metrics. Results are also proved that systematically compare the scalar and self-dual Weyl curvatures of certain almost-Kaehler 4-manifolds.

arXiv comment27 pages, LaTeX2e. This version corrects a number of minor typographical errors