%0 Journal Article
%T Weyl Curvature, Del Pezzo Surfaces, and Almost-Kaehler Geometry
%A Claude LeBrun
%J Mathematics
%D 2013
%I arXiv
%X If a smooth compact 4-manifold M admits a Kaehler-Einstein metric g of positive scalar curvature, Gursky showed that its conformal class [g] is an absolute minimizer of the Weyl functional among all conformal classes with positive Yamabe constant. Here we prove that, with the same hypotheses, [g] also minimizes of the Weyl functional on a different open set of conformal classes, most of which have negative Yamabe constant. An analogous minimization result is then proved for Einstein metrics g which are Hermitian, but not Kaehler.
%U http://arxiv.org/abs/1310.0848v2