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

Abstract

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's function for $\sqrt{P^{\prime }}$.

Final version; Corrects minor typos; This is an announcement of the main results of arXiv:1511.05013; 5 pages

References in corpus (2)

• Q-prime curvature on CR manifolds
• Extremal metrics for the $Q^{\prime }$-curvature in three dimensions

Cited by in corpus (4)

• Extremal metrics for the $Q^{\prime }$-curvature in three dimensions
• The $P^{\prime }$-operator, the $Q^{\prime }$-curvature, and the CR tractor calculus
• Functional Determinant on Pseudo-Einstein 3-manifolds
• Prescribing the ${\bar{Q}}^{\prime }$-Curvature on Pseudo-Einstein CR 3-Manifolds