Extremal metrics for the $Q^\prime$-curvature in three dimensions

Abstract

Listen

Translate article

We construct contact forms with constant Q^\prime -curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by minimizing the CR analogue of the II -functional from conformal geometry. Two crucial steps are to show that the P^\prime -operator can be regarded as an elliptic pseudodifferential operator and to compute the leading order terms of the asymptotic expansion of the Green function for \sqrt{P^\prime} .